What exactly is your threat model?
What exactly is your threat model?
On a shared computer where you perceive your peers as a threat, adding a password to syncthing web UI is probably a minor entry in a long list of things you have to do to secure your processes and data, and to ensure the kernel and programs you're running are trustable (in practice, you can't verify that with 100% confidence; they can be backdoored, out-of-date with known security flaws, etc etc).
Ensuring security in such a malicious (where your co-workers/peers are apparently a nasty bunch) shared environment is so hard that to begin with that I personally wouldn't put any sensitive data there at all.
Having an API that can reconfigure syncing being available without authentication for anything running on the machine feels backwards to me. More so for a project that focuses on security.
If anyone from the project reads this, may I recommend either encouraging users to set a password or mentioning the implications on the page about Security Principles[0]?
If your threat model is you can't trust the programs running on your computer, then maybe you should switch to a different OS, for example Debian, and stick to the package manager.