Remote control a KDE session?

I've installed KDE Connect on my Android phone, and it appears to be a default install in Kubuntu 20.04 (which runs on my desktop computer) -- but this appears to mainly be useful for transferring files between the phone and computer and using the phone screen as a touchpad pointing device for the computer.

Is there a method to use an Android phone (original Pixel, Android 10, as updated as that model can get, if it matters) to log into and remotely control KDE Plasma Desktop sessions? I have software on the Kubuntu machine that I'd like to be able to use from the phone -- and preferably when I'm not at home on the same wifi/LAN, though even on the LAN would be an improvement.

I see this as requiring something akin to the Windows Remote Desktop utility, along with an Android app that can act as a remote keyboard, display, and pointing device. I'm okay with it requiring logging into a separate session from the default one that's left open on the Kubuntu machine, though ideally I'd want that user to be able to access the same /home folder with its ~/desktop etc.