fix(sync): keep up to date url and syncSupport in local storage

[nightnei]

Related issues

• Fixes https://github.com/Automattic/dotcom-forge/issues/9816

Proposed Changes

If user connected website and then something was changed on wordpress.com side - we don't reflect changes to appdata-v1.json.
With this PR we start doing it with url and syncSupport properties.
Later I will handle staging sites in the follow up PR.

Testing Instructions

1. DON'T switch to this branch, it's necessary to do in 9-th step
2. Open wordpress.com
3. Purchase atomic website
4. Open Studio
5. Connect previously purchased website
6. Open appdata-v1.json and assert that you see:
   1. "syncSupport": "syncable"
   2. "url": <YOUR_CORRECT_URL>
7. Open wordpress.com, purchase a new domain and make it primary to your blog
8. Open Studio -> Sync tab
9. Assert that nothing changed in appdata-v1.json
10. Switch to this branch and open Sync tab again
11. Assert that you see:
    1. "syncSupport": "already-connected"
    2. "url": <YOUR__DOMAIN_FROM_6-TH_STEP>

[nightnei]

@sejas maybe it's interesting for you, since you were working around fetching sites - before we were fetching sites every time when Sync tab opens, but after latest changes we don't do it any more, instead we fetch them during starting session. So I decided to refetch them when Sync tab opens, to keep data up-to-date. With this PR we are starting syncing data between Studio and wordpress.com, specifically url and syncSupport properties. Later I am going to sync staging sites, since adding/remicing them on wordpress.com doesn't reflect it in Studio.

[stephanethomas]

I don't have any particular comment about the code. I've tested those changes, and they work well. This is good to go for me 🚢.