[Alerting UI] Replace some of ui plugin dependencies with KibanaContextProvider

[YulNaumenko]

Currently we have a bunch of plugin dependencies included to AppContextProvider. It could be replaced with KibanaContextProvider:
import { useKibana } from '../../../../../../../src/plugins/kibana_react/public';

Also some of this dependencies could be removed from ActionsContextProvider and AlertsContextProvider, because all of plugins which embedding Alerts and Actions UI also use KibanaContextProvider.

[elasticmachine]

Pinging @elastic/kibana-alerting-services (Team:Alerting Services)

[mikecote]

Duplicate issue with more information #78911 (closed as duplicate).

[mikecote]

NOTE: It could be worth investigating some start plugin APIs that return flyouts for other plugins to use (ex: getCreateAlertFlyout({..}). That way they don't have to pass in all the dependencies our plugins already have and require code directly from our plugins.

[cnasikas]

Hi @mikecote @YulNaumenko!

Cases would love to have this functionality for 7.11. I am creating the Alerts UI for the case connector and I need to use this component. The component uses the notification service. It gets it as const { http, notifications } = useKibana().services;. If I register my action type (plugins.triggersActionsUi.actionTypeRegistry.register(getCaseConnectorUI())) the service is not there. This is happening because the triggers_actions_ui plugin uses its own provider (AppContextProvider) and not the KibanaContextProvider.

Cases would need the notifications and http services.

Thanks!