[ResponseOps] Add functional tests for managing alerting rules when authenticated with an API key

[doakalexi]

We need to add functional tests for the changes introduced in this PR - #154189 Allow users authenticated with an API keys to manage alerting rules
What I'd like to see is a bunch of the following scenarios:

1. create a rule
2. make sure it's running (whatever's easiest, maybe the get event log function)
3. modify the rule with one of the methods changed in this PR
4. make sure the shape is correct after the modification, and check if it's still running
5. ideally, check to make sure any API keys in the scenario are queued for invalidation / still exist / etc, as expected - this might be hard, not sure where we store those queued-for-invalidation keys

Run every combination of methods changed, where when we create the rule, and run the method, we use every combination of api-key / login. So, something like this:

for (const createType of ['api-key', 'login']) {
  for (const mutateType of ['api-key', 'login']) {
    for (const method of ['bulk_delete', 'bulk_edit', ... ]) {
      test(createType, mutateType, method);
    }
  }
}

[elasticmachine]

Pinging @elastic/response-ops (Team:ResponseOps)