Post URLs intermittently serve ActivityPub JSON to browsers after upgrading to WordPress 7.1 (caching/content-negotiation regression)

### Quick summary

**Description**

Since upgrading WordPress core to version 7.1 (ActivityPub plugin was already on 9.2.2, unchanged across the update), I've had a report from a reader that clicking a post link from Mastodon led to a raw JSON response (the ActivityPub representation) instead of the normal HTML post page. Reloading/clicking the link again shortly after showed the correct HTML page.

This did not happen before the WordPress core update to 7.1, on the same hosting/caching setup and same ActivityPub plugin version.

**Environment**
- WordPress version: 7.1
- ActivityPub plugin version: 9.2.2
- PHP version: [si connue]
- Hosting: o2switch, using XtremCache Varnish
- Site: https://vincentbreton.fr

### Steps to reproduce

**Steps to reproduce**
- Publish a post
- A Mastodon instance/client fetches the post URL shortly after publishing (presumably for a link preview / federation), sending an Accept header that may include both `application/activity+json` and `text/html` as a fallback
- A human visitor clicking the same URL shortly after sometimes receives the JSON response instead of HTML
- The issue resolves itself after some time (presumably once the cache entry expires or is refreshed by another HTML request)

### Site owner impact

Fewer than 20% of the total website/platform users

### Severity

Moderate

### What other impact(s) does this issue have?

_No response_

### If a workaround is available, please outline it here.

_No response_

Start by reproducing the post URL request after publication with an Accept header containing application/activity+json and text/html, then compare the cached JSON and HTML responses on WordPress 7.1. Trace the ActivityPub content-negotiation and caching behavior; done means human browser requests consistently receive HTML while federation requests still receive JSON.

Written by the indexing model from the issue text.