So I couldn't find where the Mail app stores the touch bar preferences, though I probably didn't look as carefully as I could have.
And since the macOS re-install on top of the existing install didn't fix it, I opted to format the whole thing and start fresh. This, unsurprisingly, fixed it. Fortunately I didn't have much stuff on the machine yet, so I did a clean re-install of everything instead of a migration from another machine.
The moral of the story is: Do NOT attempt to customize the touch bar for the Mail.app new mail compose window. It'll kill the word prediction for the Mail app, then the more you attempt to fix/edit the touch bar (again, with a compose window open), you'll eventually corrupt the entire touch bar. Doesn't seem to affect other apps.
As I said above, I've submitted the bug to Apple, but who knows if they'll see it or even make an attempt to reproduce the error.