feat: Slack connect follow-ups from #640 review

[gewenyu99]

Follow-ups to #640. I merged that PR before this work was pushed, my mistake — the review fixes and everything below were sitting uncommitted in a local worktree while the original branch went in.

What this adds on top of #640:

• Addresses my own review comments: drops the probe timeout, requests integration:read, captures check failures to error tracking, removes the JSON note keys in favor of real comments.
• Auth runs up front in the MCP tutorial so the first screen already knows the Slack state. Esc cancels back to Choose.
• slackConnected lives in the session, checked once per flow. The Connect-Slack screen seeds from it (no nudge flash) and polls every 3s while open, tearing down timers and in-flight requests on exit.
• PickerMenu supports disabled options with an icon slot. Navigation skips them, focus revalidates when options change. Connected state renders as a green ✔ "Already connected to Slack".
• The main wizard gets the Connect-Slack step between MCP and outro — always shown, declinable.
• The Goodbye card no longer duplicates the Slack card the dedicated step shows right after.
• Ctrl+C exits cleanly: no more read EIO stack, no zombie process holding the OAuth callback server.
• Health checks only fire for programs that declare a health-check screen, and onInit hooks fire when the TUI renders rather than at store construction — tests and the playground no longer hit real status endpoints.

🤖 Generated with Claude Code

[github-actions]

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[sarahxsanders]

spotted one thing with the picker menu then you're good to go