Controller in charge of a specific type of object watches a database table representing the object type. Database table represents the desired state of things. When entries to the table are CRUD-ed, that represents a change to the desired state of things. Controller interacts with the larger system to bring the state of things into alignment with the new desired state of things.

"The larger system" is more controllers in charge of other object types, doing the same kind of work for its object types

There is an API implemented for CRUD-ing each object type. The API specification (model) represents something important to developers, like a group of containers (Pod), a load balancer with VIP (Service), a network volume (PersistentVolume), and so on.

Hand wave hand wave, Lego-style infrastructure.

None of the above is exactly correct (e.g. the DB is actually a k/v store), but it should be conceptually correct.