Why is my Mac in "Presentation Mode" after a clean reboot?
Hmm. Looks like this was because of my newly connected USB-C Dell U3219. If I disconnect and restart, I'm not in Presentation Mode.

I was on 10.15.3. Since updating to 10.15.4, this is no longer an issue.

Update - this is still happening on 10.15.4. When this happens, the two-finger swipe from the right edge to the middle no longer opens the Notification Center.