There is really nothing specific to API layer (I am assuming you mean REST API layer) in building backwards- and forwards-compatibility compared to databases. If anything, it is less powerful.
replyIt is pretty easy to do with databases as well, you just need to adopt the right mindset.
For instance, if you think having an "api/vX" of an endpoint is acceptable, then it must also be to create a duplicate table/relation — you'll have exactly the same challenges in maintaining consistency between the two, though RDBMS offer quite a bit of tooling built-in.
The difference between a rest api (or gRPC or whatever) and a database schema is the degree to which clients of either are coupled to the data model. With a rest API, you have a degree of freedom to change the data model without breaking clients. Sure, you could implement that decoupling via views (for reads) and stored procedures (for writes) within a DBMS. This is generally clunky though, in my experience
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