Gramps Web doesn’t support MySQL. It support Postgres, but for a handful of users this is usually not needed. I run my own tree with SQLite and never have problems – as long as the tools interfacing with the API don’t send exactly simultaneous requests.
But how could I recover from a locked database in future? Because parallel requests are also possible (but not very likely) when two users are changing the tree at the same time.
I honestly don’t know. Would be good to find out for sure…