Fix "Record issue doesn't stop after tapping the chips on status bar"

This issue was happening because the IssueRecordingService wasn't using
the RecordingController to start the recording, but instead was
bypassing it and using the IssueRecordingService directly. The solution
was simply to use the RecordingController, which handled the chip logic
already.

Bug: 364129809
Test: Verified that the fix works locally on my device.
Flag: EXEMPT bug fix
Change-Id: I9e3f9bac6ca11d089cb947c07d145804f916c510