You can treat SQL code as any other code and version your schema with git. Migrations can be handled with https://sqitch.org, and you can also reduce some of the work with https://www.apgdiff.com that will generate CREATE OR REPLACE function statements for you.
Also have to mention that when using PostgREST we encourage you to decouple your data schema(where your tables are) from your api schema(only views, stored procedures, computed columns), that way you can version your schemas(having "v1" schema, "v2", etc) and prevent breaking changes.
Also have to mention that when using PostgREST we encourage you to decouple your data schema(where your tables are) from your api schema(only views, stored procedures, computed columns), that way you can version your schemas(having "v1" schema, "v2", etc) and prevent breaking changes.