fix: shutdown logging again (#4886)

During deploys of 2023-08-03 we logged too much on shutdown. Fix the
logging by timing each top level shutdown step, and possibly warn on it
taking more than a rough threshold, based on how long I think it
possibly should be taking. Also remove all shutdown logging from
background tasks since there is already "shutdown is taking a long time"
logging.

Co-authored-by: John Spray <john@neon.tech>

test_runner/fixtures/neon_fixtures.py

@@ -1529,6 +1529,7 @@ class NeonPageserver(PgProtocol):
             ".*Compaction failed, retrying in .*: queue is in state Stopped.*",
             # Pageserver timeline deletion should be polled until it gets 404, so ignore it globally
             ".*Error processing HTTP request: NotFound: Timeline .* was not found",
+            ".*took more than expected to complete.*",
         ]
 
     def start(