Private CodeSandbox infinitely reloads in Safari

🐛 bug report

Preflight Checklist

• I have read the Contributing Guidelines for this project.
• I agree to follow the Code of Conduct that this project
  adheres to.
• I have searched the issue tracker for an issue that matches the one I want
  to file, without success.

Description of the problem

Sandboxes marked as 'Private' (as opposed to 'Public' or 'Unlisted') infinitely reload on Safari, which makes working in them impossible.

How has this issue affected you? What are you trying to accomplish?

I've recently tried to have pairing sessions via Live Mode with others who use Safari as their default browser, and the only workaround is to use Chrome or Firefox. To be fair, it's not a big deal for my coworkers, but my company also uses it to conduct interviews so it'd be nice to not have to ask candidates to change browsers.

To Reproduce

• Create any sandbox
• Change the permissions from 'Public' to 'Private'
• Reload the sandbox

Here's a video of changing to 'Private' and reloading. It stops immediately when I change it back to 'Public':

Link to sandbox: Freshly forked vanilla app

Your Environment

Reproduce the issue in Safari 15.2 on macOS 12.1 using the linked sandbox: change its permissions from Public to Private and reload it, then compare the behavior with Chrome or Firefox and with a Public sandbox. Trace the private-sandbox loading flow to identify the reload loop; done means Private sandboxes load normally in Safari without requiring a browser change.