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There’s a syncthing wrapper for iOS (Möbius Sync), which is free up to 20 MB of synced files. The unlimited version only costs $5 once, so might be worth it.
Otherwise I’m sure there’s ways to set a network fileshare on your PC, that you can access from your iPad (if you only need it in LAN).
Signal is probably just fine.
If you do want to use Matrix, but without matrix.org, then there are plenty of smaller public Matrix instances run by volunteers. For examples see this list. I can recommend tchncs.de