Always report healthy when instance has caught up with outstanding tasks

Once the instance has caught up with outstanding pull-replication tasks
on startup, we consider the node healthy and ready to receive write
traffic. As such, any subsequent invocations of the check should return
a healthy status, regardless of pending or inflight tasks being present.

Bug: Issue 312895374
Change-Id: I831dbb723a8a3af15eb12331e6073396534cdde8