I'm remoting into my work machine with RDP in a similar way, also using multiple (local) screens. I happen to be on CachyOS (Arch), but I would assume this works on any distro.
I just call xfreerdp3 directly with the appropriate command line options to span my local monitors which I want to use. I only use 2 of the 3 I have, as the 3rd remains for my local stuff.
Zero issues. Just works once setup.
A lot of people keep suggesting Remmina, but I couldn't get that to work even slightly. Let alone with fine grained control over monitors.