My Mac is governed by MDM from my employer, is there any privacy issue?

Definitely. Assume EVERYTHING you do on that computer is fully known to your employer. It doesn't matter if they say they can't see it, that's bullshit. Don't take their word for a damn thing, and don't rely on contracts, privacy policies or similar "paper" to protect you because you'll only know if it works _after_ you've been exploited and likely suffered the consequences.

I keep my employer's laptop off, lid shut, on the other side of the room, disconnected from power. I just use my own and tell them otherwise. 8 months and they haven't noticed (yet). If/when they do I'll just set it up to remote in from my real computer and practice some very hardcore discipline.

Yes, you shouldn't put your personal Apple ID on your work laptop.

Hi, I co-admin an MDM. Yes, it's a huge privacy issue.

You should not have any personal stuff on a work computer, let alone a work computer with MDM.

Even if we aren't purposely gathering everything (and I mean everything) for an investigation, we often accidentally run into some pretty embarrassing personal stuff by accident.

Don't do it. If not for your own privacy, for your MDM administrator.

Zero Trust.

apart from them getting to know everything what you do it is also important to understand that your employer will be liable for anything you do with their computer.

(Download something by bittorrent, even if it is a legitimate Linux distro -> no fun to explain when /when, not if/ your employer gets sued)

Don't do it.

Create a dedicated work Apple ID.

I see no benefit but there's a clear risk.

say you search for a new job using your email at your current employer...

using company computer is the same problem if you open your private emails on their machine