Has anybody tried to get this to work on a Raspberry Pi? If it doesn’t work what would be the cheapest and smallest platform this could run on?

A Flatpak build of jammr is available for testing here:
https://flathub.org/apps/details/net.jammr.jammr

It supports ARM and should run on a Raspberry Pi, but I haven't tried it myself.

A USB audio interface is probably necessary if you want good quality audio recording. This only matters if you are plugging in an instrument or microphone. If you are using software instruments then the built-in audio output is probably fine.

Please let me know how it goes!