Run the "no-default-features" tests in CI

[Velfi]

I created the "no-default-features" tests as part of #2055

In order to unblock the release, we decided not to implement a new CI mechanism to run those tests in CI. However, the tests aren't very useful if we don't start doing that.

To whomever takes this on: update CI to start running integration tests that aren't associated with a specific service and that reside in their own crate.

[Velfi]

I spoke to the examples team about moving this into their repo and they aren't interested unless we can demonstrate the usefulness of these tests as examples.