> Each site was more or less a fork of the codebase, and required a separate DB instance.
I don't believe this is true. At least as of 2016, the various sites were on a shared codebase [0], and there were two SQL Server clusters total [1], for all the various sites, chat, devops, other systems, etc.
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.
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