Sync: Add offline status indicator to push progress UI

[gavande1]

Related issues

• Fixes STU-1195

Proposed Changes

• Shows offline icon instead of info icon when user is offline during push
• Updated tooltip message to explain offline status and that sync will continue remotely

Testing Instructions

1. Start a push sync operation
2. Let the upload phase complete
3. When remote backup phase starts, disconnect from the internet (turn off WiFi/network)
4. Observe the push progress UI - it should now show:
   • An offline icon (cloud with slash) instead of the info icon
   • A tooltip explaining the offline status: "Your internet connection appears to be offline. Sync will continue running remotely. We will send you an email once it's completed."
5. Reconnect to the internet and verify the icon changes back to the info icon

Screenshot

Pre-merge Checklist

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

[wpmobilebot]

📊 Performance Test Results

Comparing c74ada4 vs trunk

site-editor

Metric	trunk	c74ada4	Diff	Change
load	7509.00 ms	5845.00 ms	-1664.00 ms	🟢 -22.2%

site-startup

Metric	trunk	c74ada4	Diff	Change
siteCreation	16114.00 ms	9055.00 ms	-7059.00 ms	🟢 -43.8%
siteStartup	3947.00 ms	3947.00 ms	0.00 ms	⚪ 0.0%

---

Results are median values from multiple test runs.

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

[ivan-ottinger]

Looks good to me and works as expected. ✅

Despite many users won't get to see this message, I think it is a helpful improvement for those who will. 🙂

[katinthehatsite]

The changes look good to me 👍 I left one minor comment regarding the wording.

[epeicher]

Thanks @gavande1 for improving this, I have tested it, and it works as expected. LGTM!