NSSL: Log and dump side padding reasoning

PeopleSpaceActivityTest is flaking because we're accidentally using the
"skinny notifs" layout when we're not supposed to.

Collect the state used to make side padding decisions, save it to dump
later, and (on debug builds) log it for debugging.

Bug: 326447757
Test: NA
Flag: NA
Change-Id: If662ad8a08e000eac40e3ea88b83a117e0c2691b