Integrate the shareable alert table in the Overview Page

[emma-raffenne]

Dependencies

• Handle empty state on the new alerts table #134885

The following two need to be confirmed (@liciavale):

• Add bulk actions in the new alerts table  #134884
• Build a shareable Search and Timerange component #134886 (The integration didn't need this ticket to be done)

📝 Summary

In order to integrate the new alerts table, it needs to support the same functionalities with the previous alerts table implementation. Once the above dependent issues are completed (search, time range and status filtering, empty state & bulk actions) we can then move on with the integration of the new alerts table in the Overview page.

[emma-raffenne]

This will need to be confirmed as the design for the overview page shows the Alerts Summary Widget, not the Alert Table. See #138887

cc @maciejforcone @jasonrhodes

Update:
Both alert table and summary must be shown in the Overview page. See #138887 for design.

cc @maryam-saeidi