Studio: Snapshot counter not updating in settings when a site is deleted

[kozer]

Fixes https://github.com/Automattic/dotcom-forge/issues/8132

Proposed Changes

This diff fixes a bug when the snapshot counter in user settings is not updated when the user deletes a site from settings tab.

NOTES:

1. The problem was created due to circular dependencies between the different hooks and useSiteDetails.
2. The issue is now fixed, by centralizing all snapshot logic in one place, and use it in useSiteDetails, where necessary
3. It can simplified further, and moved into different hooks to offload the main use-snapshots provider. However, as we have moved to another project, I leave it for a different ticket.

Testing Instructions

1. Create a site
2. Add a snapshot
3. Open user settings and ensure the counter has been increased
4. Navigate to settings
5. Press "Delete site" button at the bottom of the page
6. Ensure that after visiting settings, the counter has been decreased.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

[sejas]

I've tested it by creating, updating and deleting some snapshots, and checking the quota. Everything worked as expected.
I've added some optimizations and suggestions removing duplicated code.