Update the docs for state_periodic_save_interval (#86611)

This commit updates the docs for state_periodic_save_interval following
a question in the forums about what the consequences of this change could
be.

docs/sources/alerting/set-up/performance-limitations/index.md

@@ -67,3 +67,8 @@ can also be configured using the `state_periodic_save_interval` configuration fl
 
 The time it takes to write to the database periodically can be monitored using the `state_full_sync_duration_seconds` metric
 that is exposed by Grafana.
+
+If Grafana crashes or is force killed, then the database can be up to `state_periodic_save_interval` seconds out of date.
+When Grafana restarts, the UI might show incorrect state for some alerts until the alerts are re-evaluated.
+In some cases, alerts that were firing before the crash might fire again.
+If this happens, Grafana might send duplicate notifications for firing alerts.