fix(platform): close production performance gaps

[iamjr15]

Why

Production QA of the Cloudflare performance rollout found two concrete gaps:

• project summaries and project search results returned latestThreadId: null even when chats existed;
• the authenticated home page still started six API requests instead of the planned three.

What changed

• Replace correlated raw SQL with typed PostgreSQL lateral joins for latest project threads.
• Load model policy only when the model menu opens and keep provider choices disabled during the initial policy fetch.
• Load the composer skills catalog only when an @ mention is active.
• Load the global terminal context only after the Computer panel opens.

No schema migration or architectural boundary change is included.

Verification

• pnpm lint
• pnpm typecheck
• pnpm turbo build --force
• pnpm deadcode
• pnpm architecture:check
• pnpm turbo skills:build
• pnpm worker:performance-budgets
• Production QA on merge d1ad4ccd: Google sign-in, authenticated bootstrap, project/search response inspection, real status stream, successful GPT-5.6 Sol completion, persisted final checkpoint, and reload/reconnect.

Linear is intentionally omitted because the project has no Linear approval workflow.