We don't need two (and half) templating systems anymore, yay!
I'm keeping the changes minimal, to make the diff manageable. Some enhancements
due to a better templating system might be possible in the future.
For handling of '## ' — see the next commit.
It's lightweight and generally useful, so it should be enabled by default. But
users might want to disable it for whatever reason, and things should be fine
without it, so let's make it installable so it can be disabled if wanted.
Fixes#15175.