Move controller specs into request specs

In a recent MR some new controller specs were added, but it would be great to convert these into request spec instead (&5076)

The following discussion from !76720 (merged) should be addressed:

• @jprovaznik started a discussion:

  We are in transition from controller specs to request spec and we should avoid adding more controller specs (there is a CI warnin about this in !76720 (diffs, comment 773177692)). I missed this in previous review round. Given that this is not a blocking issue (it can be easily addressed in a follow-up) and you wanted to get this MR ASAP I'll create a follow-up for this one and proceed with merge.