Description

The alert badge (count indicator) on the server list view does not clear when alerts are acknowledged from a server tab. The badge continues showing the previous count even after the user dismisses/acknowledges all alerts.

Steps to Reproduce

1. Open Dashboard and connect to a server with active alerts
2. Note the alert badge count on the server list entry
3. Navigate to the server tab and acknowledge/dismiss the alerts
4. Return to the server list view
5. Badge still shows the previous count

Expected Behavior

The alert badge count should update (decrement or clear) when alerts are acknowledged.

Context

This is a new bug introduced with the alert badge feature (PR #182). This is not related to the previously closed Lite alert persistence issue.