Syncthing always encrypts when not local. I don't recall, but it may also encrypt locally by default (I know Resilio doesn't encrypt local by default, but I think ST does).
ST is great on battery, and I sync a lot of files/folders between my phone and desktop. When setting up a new phone, I use ST to get thousands of files into the new phone (my photos, apks, documents, media files, etc).
For example, ST has used about 6% of battery consumption over the last 24hrs - most of that is probably from syncing new backups at 2am. I also keep my entire SD card synced to my desktop using ST.
On other phones with minimal sync requirements, it's hardly noticed.
Not sure what you mean by regex support though.
Edit: It definitely uses TLS when local, I ran into a TLS version conflict on my LAN a while back.