Do you have any pointers on how that is done? I assume/hope it is just a sqlite database so the only trick is yanking the file from the phone?

Yea I saw iPhone usage was mentioned in the docs and I have no idea how that’s done. I’ve only tried through my laptop with iMessage sync by issuing

$ sqlite3 ~/Library/Messages/chat.db

and then performing some sql commands

The database file is the same across both platforms, you just need to choose the right path: https://github.com/ReagentX/imessage-exporter/blob/c73bc4d66...

You can get this file from an unencrypted iOS backup: https://github.com/ReagentX/imessage-exporter/blob/c73bc4d66...

How do I make a backup without the Cloud on Linux?

Instructions I found from Apple (https://support.apple.com/en-us/HT203977) are to use the Cloud, a Mac, or Windows +iTunes.

Maybe something like https://github.com/libimobiledevice/libimobiledevice? I'm not sure, I haven't tried to do this.

libimobiledevice definitely works for this, I've done it before.