PMS write settings on shutdown regardless of pending type

Realized that the prior refactor to write out settings is invalid
because if the message type is different, it won't write out settings.
The generic write method serializes everything, so there's just one call
to that.

Bug: 228086624

Test: presubmit

Change-Id: I96f8dda03d7160779aaf30dad75f245eb150ed3c