feat(admin): add GitHub organization installation lookup

[pandemicsyn]

Summary

• Add an employee-only Integrations page under Product & Engineering with exact GitHub organization-name, @mention, or organization-URL lookup.
• Check the Standard and Lite GitHub Apps independently, and show installation details plus linked Kilo personal accounts or organizations using existing admin detail links.
• Separate live GitHub evidence from potentially stale local associations, including suspension, pending records, missing owners, multiple records, and bounded-result truncation. A GitHub 404 is reported as no installation found, not a confirmed uninstall.
• Reuse existing server-side admin authorization and audit conventions. Lookup is read-only, uses POST to keep search input out of request URLs, and returns minimal fields with sanitized failures. No new dependencies or schema changes.

Verification

• Browser-checked the local Integrations page using synthetic identities and fixtures only.
• Checked invalid input, normalization, real local unknown-configuration/empty-record responses, and mocked installed/suspended/not-found responses.
• Checked loading controls, stale-result hiding, safe errors, retry, and encoded owner links.
• Checked responsive layouts at 375px, 900px, and 1440px.
• Verified actual HTTP rejection of anonymous callers (401) and non-admin callers (403).

Visual Changes

New Product & Engineering navigation entry and Integrations lookup page. Screenshots omitted as requested.

Reviewer Notes

• Independent read-only review and re-review completed with no remaining feature-specific blockers. Review prompted narrower wording for ambiguous GitHub 404 responses.
• GitHub 404 does not establish whether the organization exists or was renamed. Local records are never treated as authoritative installation status. Live GitHub installation responses were mocked during validation; no production records were used.
• Automated validation passed: pnpm --filter web lint, pnpm --filter web typecheck, changed-file formatting checks, and git diff --check.
• pnpm --filter web test --runInBand github-installation-lookup admin-github-router GitHubInstallationLookup: 6 suites, 46 tests passed, including authorization, audit privacy, error redaction, normalization, and database association/query-bound coverage. Database tests used an isolated worktree database prepared with pnpm test:db.
• Typecheck completed with nonblocking Rollup external-dependency warnings.