For things like stored procs, triggers, and views, there's a lot of vendor-specific (e.g. Postgres vs MySQL vs SQL Server) edge cases in syntax, introspection, and operational best practices. That's true of tables too of course, but at least the introspection part tends to be fully functional for tables in all major database systems. For other object types, introspection can be half-baked and things can get painful in general. It's much harder to design a generic declarative tool which works across multiple DBs without making sacrifices in expressiveness, safety, and ergonomics.

So most likely you're going to want a Postgres-specific tool for this, but I'm not sure one exists yet that handles everything you're looking for here.

I'm the author of a product called Skeema which does handle all this (tables, procs/funcs, views, triggers) for MySQL and MariaDB, and in my opinion this is an area where MySQL/MariaDB's relative simplicity -- in things like e.g. lack of transactional DDL -- actually makes this problem easier to solve there. For example Skeema explicitly doesn't handle data migrations because you can't atomically combine schema changes and data changes in MySQL/MariaDB in the first place.

btw when describing/searching for this, I always say "declarative" and never "state-based". "Declarative" is consistent with terminology used by other infra-as-code such as Terraform and Kubernetes. The main places I see calling it "state-based" are marketing blog posts from commercial schema management tools using an imperative migration approach (Liquibase, Bytebase, etc). To me it feels like they say "state-based" in order to make the declarative competition seem more strange/foreign...