Actually, (and I wasn’t aware of this until you mentioned it), it does support serverless connections:

https://github.com/rustdesk/rustdesk/wiki/FAQ#i-only-use-rustdesk-for-a-few-devices-on-my-local-network-with-no-internet-connectivity-can-i-still-use-rustdesk-with-direct-ip-access

So I think between cloud server, self hosted server and direct IP, OP should be covered.

RustDesk (rustdesk.com) is open source, and similar to TeamViewer, and has paid plans, including a paid self hosted option.

Did the services fail to come back due to the bad reboot, or would they have failed to come back on a clean reboot? I ugly reboot my stuff all the time, and unless the hardware fails, i can be pretty sure its all going to come back. Getting your stuff to survive reboot is probably a better spend of effort.