Find GitHub CLI on Windows when launchers have stale PATH

[TheSteelNinjaCode]

When GitHub CLI is installed after a Windows terminal or desktop launcher starts, the office inherits a PATH that cannot find gh. The elevator reports that gh is not installed even though it is installed and signed in.

Add a shared resolver that preserves PATH precedence and checks standard system, per-user, and WinGet GitHub CLI installation folders. Use it for GitHub API calls, both clone paths, setup, and account sign-in. Document Windows setup and add regression coverage for stale PATH, precedence, WinGet links, missing installations, and unchanged Unix lookup.

Validation:

• npm run typecheck and npm run build pass.
• GitHub resolver, GitHub logic, and size tests: 12 pass.
• Real gh --version succeeds with PATH limited to System32; the running patched server lists 141 repositories through floor.repos without GitHub CLI on its PATH.
• npm test encounters existing Windows failures in client-registry and shell-script clone fixtures, reproduced on unchanged origin/main. DSH, repositories and worker integration fixtures also fail and leave child processes running on unchanged main. Stopped these stalled fixtures in both baseline and full-suite runs; full-suite success is not claimed.

No client UI changes.