iOS can back up to a Mac or PC.

News to me! Where is this option described, ideally by Signal itself?

If you are alleging that Apple's own local Finder/Itunes backup of an iPhone includes Signal messages, that's not true, against reasonable user expectations, by Signal's own design choices.

Anyone who's counting on such local backups to save their histories is in for the same rude surprise I and many others have hit unaware:

https://www.reddit.com/r/signal/comments/1hgukpg/backup_and_...

And note: Signal has been misleading users about options for iOS backups for a decade! In September 2015, users were told it was "on the roadmap": https://github.com/signalapp/Signal-iOS/issues/905#issuecomm...

No option has ever existed on iOS, despite the recent announcement assuring users "Local backups still exist". They've never existed for iOS users!

Sadly not Linux tho.

If you sync an iPhone to a Linux machine, you can then save your backups on Linux.

"libimobiledevice" has CLI tools that can backup/restore iOS devices on Linux.

Do such backups retain Signal message history - unlike Apple's native local backups to MacOS?

This uses the same protocol as macOS, so same outcome. However (not sure if it helps in this case), keep in mind that different data is retained depending on whether the backup is encrypted or not (the tool supports encrypted backups too). So maybe check with encryption enabled and see if it carries over Signal messages?

It doesn't. Signal opts its data out of even encrypted local iPhone backups.