Transferring old music to new iphone

I have a lot of old music that I used to manage through iTunes that is currently on my previous iPhone X. I just got a new iPhone 13 Pro and I want to transfer that music to my new phone. I use Apple Music and figured it would be as simple as making sure “Sync Library” is checked but it is and I still get an error on my new phone when I try to play those old downloaded songs. The error says “This song is not synced across your devices”. I assume this is because the music was manually downloaded to iTunes awhile back. The PC I used in the past to manage my iTunes isn’t operational at the moment so I’m hoping to find a solution that doesn’t require that. Any help would be appreciated!