rpopken
So you mean Bullseye host + Buster guest works, Bullseye host + Bullseye guest does not work in your case? Indeed looks like a change in Bullseye then. But as stated, we do not apply any security policy, I don’t have any experience with the QEMU agent, and we do not create Bullseye images any different than Buster images in any of those regards. It happened here and there that on Bullseye some packages got dependencies removed or degraded to recommendations, while other apps, depending on them, still required those previously pulled in dependencies. Basically it would be an idea to compare the package lists between the Buster and Bullseye host, respectively reviewing the autoremoved packages after the upgrade.
Another test could be to upgrade the package on the Buster system to the new version via backports:
apt install -t buster-backports qemu-guest-agent
This version matches the one from Bullseye, so if the issue is related to his, it should be seen.
And finally, I’m not sure how communication is done, but often such things require dbus and/or logind, especially for shutdown actions. At least worth a try:
systemctl unmask systemd-logind
apt install dbus
systemctl start systemd-logind
Through, if this was really the issue, there should be some “bus not found” like errors 
.