[ResponseOps][Alerts Table] Alerts table integration in Dashboards

[cnasikas]

To improve the usability of Alerting, create alignment with the Discover++ vision, and increase visibility in Dashboards when using alerting we should be able to visualize alerts in Dashboards.

Designs: https://www.figma.com/design/c5FlBijdqWhJce2G9egO6j/New-Alert-panel-in-Dashboard--%3E-%23313?node-id=243-27879&node-type=canvas&t=YKzYDVuUHRvDn7UW-0

Blocked by: https://github.com/elastic/kibana/issues/195180

DoD

• User should be able to add a new Alerting panel to a dashboard.
• User should be able to edit the Alerting panel in a dashboard.
• User should be able to filter the view based on Solution (o11y or security), rule type, rule tags, and/or specific rules.
• User should be able to see just alerts that match my permissions.
• Users should be able to view the alerts details without leaving the Dashboard app. The default flyout will be used without supporting custom flyouts by solutions.
• Users should be able to view the rules details without leaving the Dashboard app. The default flyout will be used without supporting custom flyouts by solutions.

[elasticmachine]

Pinging @elastic/response-ops (Team:ResponseOps)