[BUG] Account marketplace "Sync automatically" never re-syncs on push; only manual "Check for updates" moves the synced commit

## Environment
- claude.ai (web) and Claude Desktop (macOS, Darwin 25.4.0), same account
- Marketplace: private GitHub repo `haydenmoorecpa/hfm-skills`, added as an **account marketplace** (Settings → Plugins → Add → Add marketplace), `.claude-plugin/marketplace.json` at repo root, one plugin with 13 skills
- Claude GitHub App installed on the account with **All repositories** access, authorized, used within the week; no repo-level webhooks
- Plugin version is generated from a content hash and bumped on every content change, so each push is distinguishable on the plugin page

## Summary
The marketplace's ⋮ menu shows **Sync automatically — "Re-syncs on GitHub changes"**, on by default. It never fires. Across ~9 hours and 8 pushes to the default branch, "Synced commit" on the marketplace card and the plugin version never moved. **⋮ → Check for updates** pulls the new commit within ~20 seconds every time, so the pipeline itself works; only the automatic trigger does not.

## Timeline (2026-09-11, US Eastern, read from the Manage marketplaces dialog on claude.ai)
| Time | Event | Synced commit shown | Plugin version shown |
|---|---|---|---|
| ~10:30 | Marketplace added | c13c5b5 | 1.2.0 |
| 12:18 | Push, version → 1.2.1 | | |
| 12:32 – 12:45 | Read 3× | c13c5b5 | 1.2.0 |
| 12:46 | **Check for updates** clicked | bfb9031 (toast "Updated to bfb9031") | 1.2.2 |
| 12:46 – 21:40 | 7 more pushes (versions up to 1.2.6) | | |
| 18:00, 20:52 | Read | bfb9031 | 1.2.2 |
| 20:52 | Sync automatically toggled **off → on** | | |
| 20:54, 20:58, 21:07, 21:40 | 4 pushes after the toggle | | |
| 21:02, 21:14, 21:24, 21:54 | Read | bfb9031 | 1.2.2 |

## Expected
A push to the repo's default branch re-syncs the marketplace (or at least the plugin page reflects the new version within some bounded interval) while "Sync automatically" is on.

## Actual
Nothing re-syncs until a human clicks Check for updates. Toggling the setting off and on does not change this.

## Desktop log observations (`~/Library/Logs/Claude/main.log`)
- `[PluginsFetcher] … 2 plugins from 2 marketplace(s)` runs roughly hourly — it lists the account's plugin snapshot, it does not re-sync the repo.
- No line resembling an automatic marketplace sync appears at any time on 2026-09-11 or 2026-09-12.
- The only refresh lines are the manual ones (`Refreshing marketplace: hfm-skills` / `Marketplace refreshed`), and those were for the **local Claude Code** clone (a separate registration of the same repo), not the account marketplace.

## Notes
- Possibly related: #86818 (Check for updates on an account-scoped git marketplace fails on first attempt — not observed here; ours succeeds first try but never runs unprompted) and #17361 (local plugin cache never refreshes).
- Happy to provide account/marketplace identifiers privately.

Start by reproducing the account-marketplace flow with an account-scoped GitHub marketplace and compare automatic syncing with the ⋮ → Check for updates path. Inspect the account marketplace sync trigger and the hourly PluginsFetcher observations in ~/Library/Logs/Claude/main.log; done means pushes re-sync within a bounded interval while Sync automatically is enabled.

索引モデルが issue の本文から書いたものです。