Open source GUI-based remote desktop package?

The problem is that to do what you are trying to do in a secure way, really needs a server component.

You don’t want to poke holes in your firewall to allow a bunch of sharing ports.

Anything with a hosted server component has a higher chance of either being commercial or at least being hosted by a commercial entity.

There are solutions like rustdesk that can be self-hosted but then you need to host an instance yourself and that isn’t really push-button “easy”.

If you want “easy”, use something like Zoom but, of course, that is commercial. jitsi used to support remote control but it was removed due to security problems with the implementation.