Studio: Indicate site deletion with loading spinner

[katinthehatsite]

Related issues

Fixes STU-1179

Proposed Changes

This PR ensures that we display a loading spinner when a site is being deleted to make it consistent with other actions such as site creation:

Testing Instructions

• Pull the changes from this branch
• Start the app with npm start
• Ensure that you have at least one site
• Navigate to the Settings tab
• Click on the ellipsis in the top right corner
• Click on Delete site
• Confirm that you can see the spinner while a given site is being deleted
• Confirm that the spinner does not appear for any other site

Pre-merge Checklist

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

[github-actions]

📊 Performance Test Results

Comparing f58638e vs trunk

site-editor

Metric	trunk	f58638e	Diff	Change
load	10821.00 ms	11255.00 ms	+434.00 ms	🔴 4.0%

site-startup

Metric	trunk	f58638e	Diff	Change
siteCreation	25633.00 ms	22671.00 ms	-2962.00 ms	🟢 -11.6%
siteStartup	10047.00 ms	9075.00 ms	-972.00 ms	🟢 -9.7%

---

Results are median values from multiple test runs.

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

[gavande1]

I have tested this and works as expected. LGTM 👍

[nightnei]

LGTM and works as expected 👍

[gavande1]

I restarted the tests