Performance is indeed a touchy subject, and I do agree that database constraints should (at least theoretically) have similar or even better performance than application layer constraints - because the database is in fact optimized specifically for that.
Modelling business entities is not the job of the data layer. I know, people will disagree on this, but I firmly believe that the data layer should not be opinionated about business logic. It is storage, and it exists to model data structures, not business structures.
As I said in my other comment, the constraints the data layer should be responsible for are relationships (in a relational DBMS), and internal integrity (that is, valid types, limits, and so on).
While I agree that a lot of people eschew an API layer, that's bad practice as well. There should absolutely be an API core that models the actual business logic.
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A few points: