[iamnbutler]

• Diagnostics list GitHub CLI between Git and Shell, read from gh auth status --hostname github.com --json hosts with the same token and environment the host's other gh calls use (now shared as github.environment()).
  • Signed in: Settings → Host → Tools shows the path and "Signed in as ".
  • Missing: "Not found" and "Install GitHub CLI, then sign in with gh auth login, to use GitHub."
  • Signed out: "Sign in with gh auth login to use GitHub." A rejected token says to run gh auth login again.
• The first-run and team-setup check (Checks) reads that entry. It says "install GitHub CLI, then run gh auth login" when gh is missing, and shows GitHub · <login> from gh. Before this change, a fresh host's welcome said "GitHub: run gh auth login" even when signed in, because hello's login arrived before gh answered and was never sent again.

Map: ^6, ^742. Part of #540: this PR adds the check. The access, avatar and dashboard effects listed in the issue are unchanged.

Smoke:

• bun types, bun run ci.
• Ran an isolated loopback host from this lane on a fresh ACE_HOME, then checked the first-run welcome and Settings → Host in headless Chromium:
  • Signed in: ✓ GitHub · iamnbutler in the welcome, and "Signed in as iamnbutler" in Tools.
  • gh off PATH: ! GitHub: install GitHub CLI, then run gh auth login, and Tools shows Not found with the install message.
  • Signed out (a gh stub that prints gh's own signed-out JSON, {"hosts":{}}): ! GitHub: run gh auth login, and Tools shows the sign-in message.

Built in Ace

No: made from Claude Code (a fix-train worker), using headless Chromium for the smoke test. Dogfooding gap tracked in #5.