Sync: Add Jetpack connection status check

[ivan-ottinger]

Related issues

• Resolves STU-613

Proposed Changes

• introduce new SyncSupport case: jetpack-disconnected
  • add related Check connection CTA linking to the Sync modal
  • ensure related warning is displayed in the Sync tab for already-connected sites
  • ensure that sites without proper Jetpack connection cannot be linked with local Studio sites

Sync tab	Sync modal

Testing Instructions

1. Check out the PR branch and build the app with npm install && npm start.
2. Create a test Pressable site, connect it to your WPCOM account using Jetpack.
3. Head over to the Sync tab of a local Studio site and connect the test Pressable site to the local site.
4. Navigate to your Pressable dashboard and delete your test site there (this can be done from the bottom of the Site Actions section):

5. Review the Sync tab in Studio. There should now be information that the site is unreachable.
6. Open the Sync modal. The site should be disabled and have Check connection link displayed on the side.

Pre-merge Checklist

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

[github-actions]

📊 Performance Test Results

Comparing 836a441 vs trunk

site-editor

Metric	trunk	836a441	Diff	Change
load	9298.00 ms	9396.00 ms	+98.00 ms	🔴 1.1%

site-startup

Metric	trunk	836a441	Diff	Change
siteCreation	13019.00 ms	17096.00 ms	+4077.00 ms	🔴 31.3%
siteStartup	3927.00 ms	4924.00 ms	+997.00 ms	🔴 25.4%

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Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change