Welcome!
When you run the whole desktop in a container, with hardware acceleration, the process is quite involved. You are likely going to use some stock distribution image. But those images are not designed to work inside a container. They may be looking for VTs but those are not available. And so on.
If only there was a way to find those small issues, selectively change the code, package again the fixed programs and generate new containers. That’s exactly what @tarruda did. See here, Tutorial: How to run a full desktop environment on LXD
Here is how it looks. I just took the screenshot.
Do you need to generate such desktop container images? Apparently there are such desktop container images. I am not sure how they are supposed to be used.
$ incus image list images:desktop-kde -c ldt
+------------------------------------------+--------------------------------------------+-----------------+
| ALIAS | DESCRIPTION | TYPE |
+------------------------------------------+--------------------------------------------+-----------------+
| opensuse/15.4/desktop-kde (1 more) | Opensuse 15.4 amd64 (20240515_04:20) | CONTAINER |
+------------------------------------------+--------------------------------------------+-----------------+
| opensuse/15.4/desktop-kde (1 more) | Opensuse 15.4 amd64 (20240515_04:20) | VIRTUAL-MACHINE |
+------------------------------------------+--------------------------------------------+-----------------+
| opensuse/15.5/desktop-kde (1 more) | Opensuse 15.5 amd64 (20240515_04:20) | CONTAINER |
+------------------------------------------+--------------------------------------------+-----------------+
| opensuse/15.5/desktop-kde (1 more) | Opensuse 15.5 amd64 (20240515_04:20) | VIRTUAL-MACHINE |
+------------------------------------------+--------------------------------------------+-----------------+
| opensuse/tumbleweed/desktop-kde (1 more) | Opensuse tumbleweed amd64 (20240518_05:14) | CONTAINER |
+------------------------------------------+--------------------------------------------+-----------------+
| opensuse/tumbleweed/desktop-kde (1 more) | Opensuse tumbleweed amd64 (20240518_05:14) | VIRTUAL-MACHINE |
+------------------------------------------+--------------------------------------------+-----------------+