[latk]

Yes, what you say is more precise than what I said. They did a lot of fixing and by now nearly all sites use the same codebase (incl frontend), apparently with feature toggles for some sites (e.g. Stackapps or Meta have unique mechanics but run on the same software). The only surviving forks are probably Area51 and their Enterprise product. Previously, frontend/layout had diverged though, which prevented rapid rollout of new UI features[1]. One of the perks of a graduated site used to be a custom design (not always just CSS changes).

Sites don't need separate database servers but separate database schemas, which is also why migrations between sites are still quite broken. Many processes around launching a new site appear to be very manual.

[1]: https://meta.stackexchange.com/q/307862