RustDesk sort of fits the bill. It’s open-source, has 2FA, can be self-hosted (but not needed), the client runs on anything, but the main issue here is that no amount of workarounds will make an untrusted machine any less untrusted, you’re essentially extending the display and input from a dubious machine into your own.
If you’re really worried about the security aspect, my suggestion would be to only use your phone as the client, and if you need to do anything more complex, use a Bluetooth keyboard connected to it. There are some foldable keyboards that don’t take too much space and are not terrible.