Add integration tests to compose commands to ensure dependency order is followed

### What is the problem you're trying to solve

To avoid issues like #1658, we should have integration tests for some compose commands to ensure dependency order is followed (both in-order or reverse-order dependency).

https://docs.docker.com/compose/startup-order/

Some commands include `compose up|down|restart|stop` (not a full list)

### Describe the solution you'd like

- [ ] Check the list of compose commands that require either in-order or reverse-order dependency, and make sure they're implemented in the codebase.
- [ ] Add integration tests for these commands. For example, `compose up svc0` should also `up` services that `svc0` depends on.

### Additional context

_No response_