Refactor kibana-react context

[streamich]

• Refactor kibana-react global context
  • Remove .notifications and .overlays objects from context.
  • Lift .services object up.
  • Possibly add useNotifications and useOverlays hooks instead of .overlays and .notifications objects.
• Update docs to remove examples of passing all of core to the provider
  • As discussed in [discuss] Direct dependency on NP code in low-level components...? #53029, passing all of core to the provider encourages tight coupling to the UI, which can be problematic, and we want to avoid recommending this to devs.
  • Examples using this approach should be removed from the docs; instead we should only show examples where pieces of core are explicitly passed to the provider.

[elasticmachine]

Pinging @elastic/kibana-app-arch (Team:AppArch)

[lukeelmers]

I'm tracking remaining new platform migration items over in #51560, and one of those includes proposed updates to kibana_react based on the discussion in #53029.

Should we include those in the scope of this issue, or track separately?

[ppisljar]

Thank you for contributing to this issue, however, we are closing this issue due to inactivity as part of a backlog grooming effort. If you believe this feature/bug should still be considered, please reopen with a comment.