Syncthing does not need a server to work over the LAN, and I think you can set it to only use peer discovery over a LAN. You can disable pubic servers, but data sent through them is encrypted anyway.
Syncthing + KDE connect does a lot.
The only issues I have had is that I cannot ensure that both are always running on android.
Oh for sure, Syncthing absolutely works peer to peer. But I find it useful to have a central always-online hub for clients to sync to.
For example, imagine you save a file on your laptop then put it to sleep. You turn on your desktop and the file isn't there because the laptop is now asleep. Having a central 24/7 Syncthing server allows the share to always be available.
Syncthing + KDE connect does a lot.
The only issues I have had is that I cannot ensure that both are always running on android.