[BUG] Cowork: "Check for updates" on private Git marketplace uninstalls all plugins

Description

Clicking "Check for updates" on a private Git marketplace in Cowork causes all installed plugins from that marketplace to become uninstalled. After the sync completes and you navigate back to the plugins list, every plugin shows as not installed and must be manually reinstalled one by one.

Steps to Reproduce

1. Have a private Git marketplace (cowork-plugins) with multiple plugins (8 in my case) all installed and working
2. Go to Settings → Plugins → click the marketplace name → "..." → "Check for updates"
3. Marketplace syncs to a new commit successfully
4. Navigate back to the plugins list
5. All plugins now show as uninstalled — no "Manage" buttons, must click install on each one individually

Expected Behavior

"Check for updates" should sync the marketplace repo and update any plugins with new versions, while preserving the installed state of all plugins.

Actual Behavior

The marketplace sync wipes the installed-plugins registry. All plugins must be manually reinstalled after every "Check for updates" action.

Frequency

Happened twice in one session (not a one-off). Each time "Check for updates" was clicked, all plugins were uninstalled.

Environment

• Platform: macOS (Apple Silicon, Mac Studio)
• Cowork version: Latest as of March 23, 2026
• Marketplace type: Private Git repo added via "Add marketplace by URL" with embedded GitHub token
• Number of plugins affected: 8 (ai-news-digest, deep-memory, iac, linkedin-triage, logi, porres, slack-triage, whatsapp-triage)

Additional Context

• The marketplace sync itself works correctly — the "Synced commit" hash updates to the expected commit
• The plugin files in the marketplace repo are intact and unchanged (verified via git diff)
• The issue appears to be a state management bug where the sync operation resets the installed-plugins registry
• Possibly related to #14815 (plugins installed but not appearing) and #20661 (enabledPlugins not updated), though this is a distinct regression where previously-working plugins are actively removed

Screenshots

After clicking "Check for updates", all plugins lose their "Manage" button and show as available for install rather than installed.