Automatic merge from submit-queue (batch tested with PRs 52097, 52054)

Move paused deployment e2e tests to integration

**What this PR does / why we need it**:

**Which issue this PR fixes** *(optional, in `fixes #<issue number>(, fixes #<issue_number>, ...)` format, will close that issue when PR gets merged)*: xref #52113

**Special notes for your reviewer**:

**Release note**:

```release-note
NONE
```