Whenever I create a new profile for testing, I get a message pretty shortly thereafter that DoH was enabled (it drops from the address bar and has the option to turn it off). Maybe that only happens automatically in new profiles and not in existing profiles?

This is not a new profile. this is a from scratch install.

If you are installing from scratch, then Firefox will create a new profile. If you do not connect to a Firefox Account and transfer settings from another installation of Firefox, then it should have completely default settings and at some point, assuming the criteria in the code are met, you should get the notification that DNS over HTTPS was switched on.

What I did is I installed from scratch and looked in the Preferences, general, network settings expecting to see "enable DNS over https" already checked. In my case it was not.

I think it is turned on after some checks are run, but I haven't researched it in detail.

I have not seen this on my install. Why is it not preconfigured?