Quite a while ago I worked on two different Microsoft SQL systems that had hundreds of stored procedures, we had a version control and migration system that was ‘good enough’.
You can think of stored procedures like an API that one would provide over http, except it is over the ODBC, JDBC or whatever db interface you use. Surely you could make a web API that is a thin veneer over some stored procedures.
You can do a lot in a stored procedure with the particular advantage of a low latency location close to the database engine for good transaction performance.