Maybe with Xpra you could do something like that

Some ideas for the future

Xrdp fail… plain and simple…

Xrdp usually works fine, you should try to find any specific error messages or logs. Xrdp also runs a service so you could also see if the service itself is running or what it's status is (systemctl status xrdp).

For me Xrdp did fail when I initially tried to run it. I don't remember the exact error being produced but there was something wrong with the port number xrdp wanted to use.. in the end I had to stop the service, edit /etc/xrdp/xrdp.ini and set the port to a specific port number without using vsock. xrdp by default was set to use vsock ports which wasn't working for for me.

Sounds like you want something like X11 forwarding. I have never used it, but I believe it is proper remote desktop, not sharing.

Xrdp won't work if there is already an active user session locally with the same user account that is trying to connect remotely.

I think xvnc does this with vnc. If using gnome start gnome-remote-desktop with systemctl --user start gnome-remote-desktop then use grdctl to set it up (or the settings gui). I've had luck with rdp on a Wayland session this way.

VNC? You have your choice of servers, and clients are ubiquitous.

A big gotcha is that you need to be careful with encryption/security, as in classic UNIX style VNC does one thing (remote desktops). It's easy to forward over ssh though.

You can also use VNC to share, which is not what you want; this depends on the type of server/settings. But you can definitely create a new virtual X11 session and access it remotely.