I don't expect it is a problem in Virtualbox as you assume, since I use exactly the same VBox release in Ubuntu 22.04 LTS; Ubuntu 20.04 LTS and Fedora 36. I only have a problem with the 22.10 systems using the latest gdm3. I've tried Ubuntu Mate 22.10 and that one worked fine with Virtualbox 6.1.3x.
In the begin of Ubuntu 22.10 I had no issues and everything worked fine, it went wrong after an update of the development edition, somewhere in August. I expect that gdm3 changed the way, in which they start/check the driver, so I would be looking for an incompatibility between gdm3 and Virtualbox 6.1.3x, introduced by a change in gdm3.
I don't expect it is a problem in Virtualbox as you assume, since I use exactly the same VBox release in Ubuntu 22.04 LTS; Ubuntu 20.04 LTS and Fedora 36. I only have a problem with the 22.10 systems using the latest gdm3. I've tried Ubuntu Mate 22.10 and that one worked fine with Virtualbox 6.1.3x.
In the begin of Ubuntu 22.10 I had no issues and everything worked fine, it went wrong after an update of the development edition, somewhere in August. I expect that gdm3 changed the way, in which they start/check the driver, so I would be looking for an incompatibility between gdm3 and Virtualbox 6.1.3x, introduced by a change in gdm3.