Ensure that staging sites display a Staging sticker from the moment they are created

[fredrikekelund]

Related issues

• Fixes https://github.com/Automattic/dotcom-forge/issues/10308

Proposed Changes

As reported in https://github.com/Automattic/dotcom-forge/issues/10308, newly created staging sites display a Production sticker in the Sync tab. This happens because the /sites API endpoint returns the wrong value for the is_wpcom_staging_site prop until the site setup is completed. The problem was also made worse by the reconcileConnectedSites function not refreshing the value for isStaging.

This PR changes the logic in transformSitesResponse so we look at the wpcom_staging_blog_ids arrays of other sites to determine if the given site is a staging site. This data appears to be stable from the moment a new staging site is created. For good measure, I've also updated reconcileConnectedSites to refresh the isStaging value.

Testing Instructions

1. Log in to WordPress.com in Studio
2. Connect a Studio site to a WordPress.com site
3. If the site already has a staging site, delete it
4. Go to wordpress.com/sites and create a new staging site for the site in question
5. Open Studio again and periodically switch between the Share and Sync tabs (this triggers a new fetch from the /sites API endpoint)
6. Ensure that when the staging site appears in the Sync tab, the sticker to the left says Staging (see screenshot below for clarification)

Pre-merge Checklist

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

[nightnei]

LGTM and works well - confirms that even if site was marked as Production in Trunk, then after switching to this branch it's fixed ("stage" badge is rendered)