Sync: preserve Pressable metadata in reconciliation fallback

[gcsecsey]

Related issues

• Fixes STU-1944
• Related to STU-1977

How AI was used in this PR

Claude investigated the issue, helped reduce it against WPCom with a test Pressable site, and implemented the fix.

Proposed Changes

When the Sync tab loads, Studio refreshes connected-site metadata from page 1 of /me/sites and fetches any connected site missing from that page individually via rest/v1.1 /sites/{id}. The single-site endpoint never returns hosting_provider_guess or environment_type, these are wpcom decorations that exist only on the /me/sites endpoints, even when explicitly requested via fields. Because Pressable support is derived from hosting_provider_guess, a successful fallback response reclassified a known Pressable site as unsupported (and could misfile staging sites), and reconciliation persisted that downgrade. Accounts with more than one page of sites, eg. the 80-site agency in STU-1977, hit this on every Sync tab load.

• The supplemental fetch now falls back to the stored connected site's isPressable / staging metadata when the response lacks those fields, instead of recomputing sync support from incomplete data.
• Deletion and permission changes are still detected from the response, only the missing provider metadata is preserved, so a genuinely deleted site or lost permissions still downgrade correctly.
• A jetpack counterpart (adding hosting_provider_guess/environment_type to the single-site endpoint) is being prepared separately, this guard protects all reconciliation paths regardless.

Testing Instructions

1. Run the unit tests: npm test -- apps/studio/src/modules/sync/lib/tests/build-supplemental-sync-site.test.ts
2. Manual verification (the bug needs a connected Pressable site that is NOT on page 1 of /me/sites):
   1. Connect a local site to a Pressable site on an account with 20+ sites (or temporarily lower perPage in apps/studio/src/stores/sync/wpcom-sites.ts to force the fallback).
   2. Reload the Sync tab.
   3. Before this change: the connected site shows "appears to be deleted or is currently unreachable" and its stored record flips to syncSupport: "unsupported", isPressable: false in ~/.studio/app.json. After: it stays recognized as a connected Pressable site and remains syncable.

Pre-merge Checklist

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

[wpmobilebot]

📊 Performance Test Results

Comparing ca17908 vs trunk

app-size

Metric	trunk	ca17908	Diff	Change
App Size (Mac)	1345.48 MB	1345.48 MB	+0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	ca17908	Diff	Change
load	762 ms	1119 ms	+357 ms	🔴 46.9%

site-startup

Metric	trunk	ca17908	Diff	Change
siteCreation	6495 ms	6496 ms	+1 ms	⚪ 0.0%
siteStartup	1861 ms	1862 ms	+1 ms	⚪ 0.0%

---

Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change (<50ms diff)