My go to solution on Android is an open source file browser app called Material Files that has a simple FTP server built-in. Start the server (note the IP and port) then connect over local WiFi using native File Explorer in Windows to easily browse and transfer between phone and desktop
I'm sure something similar can be done with iOS and Linux but probably in a less intuitive manner. I don't do Apple but this looks like it has potential to be part of the solution.
https://apps.apple.com/us/app/fe-file-explorer-file-manager/...
For your use case I would look at SFTP and use the ShellFish app
There are similar apps that add WebDAV servers to FIles. There are a number of media players and text editors that provide built-in WebDAV support
I have also used other apps to share between Linux and iOS: DropBox, Resilio Sync
SyncThing is now supported via the app Möbius Sync. (But I have yet to try it)
Unfortunately, as I have just learned, they stopped offering the software for sale https://panic.com/blog/the-future-of-transmit-ios/.
Disappointing.
That said, I will continue to use Transmit because I paid for it and it does its job well.
From this thread, it appears that secureshellfish may be a good equivalent.
An open Apple AirDrop implementation written in Python
Using AirDrop (proprietary protocol) hacks can (and has) break at any iOS release.
https://extensions.gnome.org/extension/1319/gsconnect/
I had issues with it, but may work for you.
Peer to peer (P2P) file sharing allows users to access media files using a P2P software program that searches for other connected computers on a P2P network to locate sought files