Move mp3 between iPads to use in Music

I have music on an old iPad which were transferred to it via iTunes (mp3) on an iMac desktop and which are visible in the Music app. I upgraded to a new iPad and synced via iCloud etc. However none of the content from the previous iPad can be played on Music app on the new iPad. The content is listed on Music but not playable. I can only play content that has been purchased from the store.

Is my only option to add mp3 content to my new iPad to connect to a desktop PC with iTunes/Music?

I can’t even find a way to transfer mp3s from an external ssd.

I am a bit shocked that I can’t seem to easily transfer mp3 content that I own onto the new iPad from the old!