You can turn off anything but sync connections. This does come at a cost, however: This functionality is there for a reason - it provides connectivity in less-than-perfect network setups.
However, if you feel you are a power user who can configure the network by itself, you are free to turn (basically) everything off:
- Turn off global discovery
- Turn off local discovery
- Turn off NAT traversal
- Turn off relaying
- Turn off upgrade checks (if enabled in your build)
- Deny usage reporting
- Turn off crash reporting in advanced options
- Configure static addresses for syncthing to connect to
Enjoy your “silent” syncthing. It will however be unable to connect to any peers not reachable via a direct, manually configured, connection.