Information on the music from the press kit and 'The Art of' book. There isn't a single mention of the second new song which probably means it was cut from the film.

I'm still holding on to a tiny bit of hope that it'll be featured on the soundtrack but chances are looking slim.
From the press kit:
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While director Guy Ritchie had never helmed a musical prior to “Aladdin,” his films are heavily influenced by music. “This is a musical in its purest traditional form,” he says, “and I liked the challenge. I didn’t try to be too ambitious or try to reinvent the wheel in terms of a musical, but I did want it to feel like it was fresh enough while still keeping the original tone of the first film.”
The score and songs by eight‐time Academy Award® winning composer Alan Menken and Oscar‐ winning lyricists Howard Ashman and Tim Rice from the 1992 film are perfect as is, but Ritchie wanted to make them feel more contemporary, both lyrically and musically…an idea that Menken embraced wholeheartedly. The songs in the animated film were embedded in the music of the Arab world with flourishes of jazz here and there. Menken’s new arrangements incorporate pop elements and showcase the musical talents of Will Smith.
The lyrics for “Prince Ali,” the film’s biggest song‐and‐dance production number, were tailored to better fit the actor’s persona. Says Smith, “‘Aladdin’ is a rare combination of cinematic tools. Very few films have singing, dancing, drama, comedy, action and special effects…all those elements in a single movie, and we have it in a single scene.”
“Guy really wanted to take chances with the music but at the same time he was deeply respectful of the original songs,” continues Smith. “He knew how he wanted it to sound and how he wanted it to feel but gave me the freedom to use my hip‐hop background and bring a fresh vibe to it.”
The live‐action score is very symphonic and resonant of old Hollywood in many aspects. “Most of the time Guy likes things to be very spare, but there are times when the score just explodes,” says Menken. “It is obviously pulled from the themes of the songs, almost exclusively, but it is much more live action in its textures and its tone.”
“Arabian Nights” is now a complete musical number that serves as an introduction to the story and its enchanted setting. Menken worked with Oscar®‐and Tony Award®‐winning songwriters Benj Pasek and Justin Paul (“La La Land,” “Dear Evan Hansen,” “The Greatest Showman”) to create new lyrics. “The job really was to be following along with the camera as it soars through Agrabah, setting up this world for the audience,” says Menken. “We rewrote some of the lyrics to go with the visuals that Guy had in mind, introducing Jafar and basically setting the stage for the rest of the film. It’s a much bigger, much more ambitious number than it was originally.”
For Pasek and Paul, working with the legendary composer was the opportunity of a lifetime. “Alan and Howard were our childhood heroes…they wrote the songs that made us want to be songwriters,” says Pasek. “We think the reason our generation is so in love with musical theatre and the reason this resurgence is happening right now is because of Howard and Alan. We grew up loving musicals and musical theatre storytelling and that’s because of what these guys wrote.”
“When we were first starting out and someone would ask us what we wanted to do or who we wanted to be, it was always, ‘We want to be Alan Menken, Howard Ashman. We want to write for Disney, like for a Disney animated musical…that’s our dream,’” says Paul.
And the admiration is mutual. “Benj and Justin are like my progeny, so to speak; they are wonderful,” says Menken. “I’m tough on writers, but these guys are really, really good. I wanted this to be a real collaboration between Justin and Benj and me, not just, ‘Oh, Alan Menken and the next collaborators or whatever,’ that wasn’t the point. The song is a collaboration of our styles, as it should be.”
“Speechless” is an original new song written by Menken and Pasek and Paul, performed by Jasmine, who is ready to find her voice. “It starts with a solo piano, very intimate, and really gets into the soul of Jasmine,” explains Menken. “And then as it builds, it builds in the arrangement and the intensity and then at the end comes back full circle to that intimate piano with her voice reaching out over it. It has a beautiful arc to it, but the sound is orchestral and pianistic.”
“This is Jasmine’s big breakout song where she decides she is going to stand up for what she believes in,” says executive producer Marc Platt (“Mary Poppins Returns”), who worked with Pasek and Paul on “La La Land.” “The song parallels her arc in the story, sung timidly by Jasmine early on and then as a big empowering moment later in the film. Jafar has seized power as her father stands by helpless, and she finally has the strength to tell him what she envisions for her future.”
“As the script was developing, it became clear that this Jasmine was going to be more powerful and outspoken than ever and that it was time for her to have a big number,” says Paul. “Her character was emerging as someone who would have this moment to really stand up and say, ‘I do have a voice, and I will not remain speechless.’”
“This is a woman who is being told who she has to be and how she has to live in the world, and then she doesn’t have a voice,” adds Pasek. “So it made a lot of sense for this really strong woman that so many girls have grown up loving to talk about reclaiming her own power.”
The choreography designed by Jamal Sims (“Hairspray,” “Step Up”) was somewhat contemporized as well. Both “Prince Ali” and “Friend Like Me” feature break‐dancing moves, giving them a modern feel and sense of authenticity, too. “These are both big performance pieces,” says producer Dan Lin. “It was both the Genie’s time to shine and the perfect opportunity for Will to show how multi-talented he is‐he has to act, sing and dance in the iconic set piece.”
For “One Jump Ahead” performed by Aladdin as he and Jasmine are being chased through the streets of Agrabah, the choreographed moves were fast‐paced, athletic and more appropriate for a Guy Ritchie film. “We never intended for Aladdin to dance in that song,” Sims says. “It is more of a stylized action sequence. There is a lot of movement, but the moves belong more in the stunt category.”
From the Art of book:
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In the original film, the introductory song "Arabian Nights" is sung by an old merchant known as the peddler, who sets the scene for the magical world of Agrabah. Lyricists Benj Pasek and Justin Paul wrote new lyrics for the song to reflect the change in who was singing the song.
"It was not someone who was living in Agrabah; it was someone who was coming to this city," says Paul. "We were tasked with giving the audience a visceral, stimulating vision of what this film's Agrabah is: a sort of meeting place of cultures. We wrote lyrics about the spices, the people bartering, and the bazaars because we wanted to color the experience for viewers as they're being welcomed into the world of Aladdin."
"With new lyrics from Pasek and Paul, 'Arabian Nights' is now twice as long as what is in the original movie," notes Sullivan. "As soon as we played the new instrumental track for Will, he yelled, 'This is the way I wanna open all my concerts!' It's just so bold and cinematic."
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One of Jasmine biggest moments in the film comes in the form of a new song written by composer Alan Menken and lyricists Benj Pasek and Justin Paul. Frustrated by being silenced, Jasmine unleashes a powerful ballad that allows her to find her voice again. The songwriters came up with the idea while working in Menken's studio and went through a few versions before landing on the final arrangement.
"We've been playing with arrangements a lot," Menken says. "We had a very pop-oriented arrangement initially, which I think works beautifully, except that it didn't feel in keeping with the fabric of the rest of the score. Instead, we've gone with a more orchestral version. It'll feel much more like a piece from the score, and I think it's that much more integrated."
When they finally played the song for music supervisor and producer Matthew Rush Sullivan and music editor Chris Benstead over the phone, the impact was immediate. "As soon as we heard it, we thought, 'Wow that's it, that's it,'" Sullivan remarks. "She's been told, growing up, she should be seen and not heard. She finds her voice throughout the movie, and at the end she puts her foot down, and says, 'I'm not going to go speechless.' It's one of the biggest, strongest moments of the movie."
Alan Menken adds, "We really had to work with the book to plant the seeds of her feeling intimidated and feeling like she's not allowed to speak her mind, and have the song come at just the right moment when she says, 'No, I will not remain speechless anymore.'"
"We were really inspired by the original movie," Benj Pasek notes. "The 'ahah' moment for us was when we went back to the source material. Jafar says condescendingly to Jasmine late in the film: 'You're speechless, I see. A fine quality in a wife.' It felt right for her to make a declaration that she would not be subjugated in that way. It was a real opportunity for her to stand her ground and sing about those philosophies, and felt like a natural extension of this very strong, powerful, and determined Disney princess. I think people gravitate to Jasmine because she is such a strong female character, and we were inspired by that and aimed to give her a song, and a moment, that matched her power."
While the team did pre-record the vocals for the scene, Sullivan also prepped actress Naomi Scott to perform the song live on set. "We really wanted to capture Naomi's best performance on the set and give her the flexibility to deliver a performance that is true to the emotions that she's feeling in that very moment," he notes.
"All the crew had goose bumps when she sang 'Speechless' on the stage," executive producer Kevin De La Noy says. "All of us just looked at each other thinking, 'We just witnessed history.' It took everyone's breath away. Everyone just knew that that was extraordinary. And it's not just the lyrics of the song — they were great, and the music is great — it's what she then did with it."
Scott was able to tap into Jasmine's intense emotions during the evocative, empowering musical number, accurately demonstrating this major turning point for Jasmine.
"She's shut down by Jafar throughout the movie, and she really wants to lead, and she's trying to persuade her father to see her in that light," Scott says of Jasmine. "This song is an expression of her just not raking it anymore. It's that moment of realization of who you are. That actually, as a woman, you already hold so many amazing qualities and skills that are strong. Having feminine qualities is really strong and amazing and actually makes you a better leader and actually helps you see the world in a different and a better way."