What do you know... Shortly after posting this, I found a thread in the Gmail help forum with a solution that worked for me, by user Nico P.
Quoting here, for reference:
If you look at your folders from your outlook account you'll notice
that there is a folder named "Trash" (or another equivalent) and
another folder that is the actual folder for ...
At the end, I settled with Syncthing. So, how does it fulfil my requirements:
It uses encryption. I didn't analyse how secure it is, so this is more matter of trust, but at least it shouldn't send data unencrypted.
Works exceptionally well. Local LAN detection seems reliable and is able to connect clients directly. I use it also at work (...