[Bug] Teams messaging uses hardcoded default directory instead of actual team name in tmux backend

Bug Description
Disclaimer: claude code generated this.
Teams bug (tmux backend only — not in-progress mode):

1. Teammate→lead messages go to wrong directory: When a teammate uses SendMessage to message team-lead, the message is

written to ~/.claude/teams/default/inboxes/team-lead.json instead of
~/.claude/teams/{actual-team-name}/inboxes/team-lead.json. The default team directory gets created even if no team by that
name exists.

1. Teammates don't poll inbox while idle: After a teammate finishes a turn and goes idle, it never checks its inbox for new

messages. Messages from the lead land in the correct file (~/.claude/teams/{team}/inboxes/{teammate}.json) but sit unread.
The only way to trigger processing is typing directly into the tmux pane.

Both issues are specific to the tmux backend. In-progress mode works correctly.

Environment Info

• Platform: darwin
• Terminal: tmux
• Version: 2.1.33
• Feedback ID: 13836a8f-15c1-40f6-ac38-11b03fcb0175

Errors

[{"error":"Error: Tool Teammate not found\n    at xn_ (/$bunfs/root/claude:1790:5881)\n    at v1 (/$bunfs/root/claude:668:20765)\n    at U6 (/$bunfs/root/claude:668:39157)\n    at Yb (/$bunfs/root/claude:668:49776)\n    at Mx (/$bunfs/root/claude:668:86026)\n    at iT (/$bunfs/root/claude:668:85998)\n    at bdT (/$bunfs/root/claude:668:85840)\n    at dd (/$bunfs/root/claude:668:81240)\n    at nR (/$bunfs/root/claude:668:6276)\n    at R0A (/$bunfs/root/claude:661:13953)","timestamp":"2026-02-06T01:57:14.821Z"},{"error":"Error: Tool Teammate not found\n    at xn_ (/$bunfs/root/claude:1790:5881)\n    at v1 (/$bunfs/root/claude:668:20765)\n    at U6 (/$bunfs/root/claude:668:39157)\n    at Yb (/$bunfs/root/claude:668:49776)\n    at Mx (/$bunfs/root/claude:668:86026)\n    at iT (/$bunfs/root/claude:668:85998)\n    at bdT (/$bunfs/root/claude:668:85840)\n    at dd (/$bunfs/root/claude:668:81240)\n    at nR (/$bunfs/root/claude:668:6276)\n    at R0A (/$bunfs/root/claude:661:13953)","timestamp":"2026-02-06T01:57:14.822Z"},{"error":"Error: Tool Teammate not found\n    at xn_ (/$bunfs/root/claude:1790:5881)\n    at v1 (/$bunfs/root/claude:668:20765)\n    at U6 (/$bunfs/root/claude:668:39157)\n    at Yb (/$bunfs/root/claude:668:49776)\n    at Mx (/$bunfs/root/claude:668:86026)\n    at iT (/$bunfs/root/claude:668:85998)\n    at bdT (/$bunfs/root/claude:668:85840)\n    at dd (/$bunfs/root/claude:668:81240)\n    at nR (/$bunfs/root/claude:668:6276)\n    at R0A (/$bunfs/root/claude:661:13953)","timestamp":"2026-02-06T01:57:14.825Z"},{"error":"Error: Tool Teammate not found\n    at xn_ (/$bunfs/root/claude:1790:5881)\n    at v1 (/$bunfs/root/claude:668:20765)\n    at U6 (/$bunfs/root/claude:668:39157)\n    at Yb (/$bunfs/root/claude:668:49776)\n    at Mx (/$bunfs/root/claude:668:86026)\n    at iT (/$bunfs/root/claude:668:85998)\n    at bdT (/$bunfs/root/claude:668:85840)\n    at dd (/$bunfs/root/claude:668:81240)\n    at nR (/$bunfs/root/claude:668:6276)\n    at R0A (/$bunfs/root/claude:661:13953)","timestamp":"2026-02-06T01:57:14.826Z"},{"error":"Error: Tool Teammate not found\n    at xn_ (/$bunfs/root/claude:1790:5881)\n    at v1 (/$bunfs/root/claude:668:20765)\n    at U6 (/$bunfs/root/claude:668:39157)\n    at Yb (/$bunfs/root/claude:668:49776)\n    at Mx (/$bunfs/root/claude:668:86026)\n    at iT (/$bunfs/root/claude:668:85998)\n    at bdT (/$bunfs/root/claude:668:85840)\n    at dd (/$bunfs/root/claude:668:81240)\n    at nR (/$bunfs/root/claude:668:6276)\n    at R0A (/$bunfs/root/claude:661:13953)","timestamp":"2026-02-06T01:57:14.827Z"},{"error":"Error: Tool Teammate not found\n    at xn_ (/$bunfs/root/claude:1790:5881)\n    at v1 (/$bunfs/root/claude:668:20765)\n    at U6 (/$bunfs/root/claude:668:39157)\n    at Yb (/$bunfs/root/claude:668:49776)\n    at Mx (/$bunfs/root/claude:668:86026)\n    at iT (/$bunfs/root/claude:668:85998)\n    at bdT (/$bunfs/root/claude:668:85840)\n    at dd (/$bunfs/root/claude:668:81240)\n    at nR (/$bunfs/root/claude:668:6276)\n    at R0A (/$bunfs/root/claude:661:13953)","timestamp":"2026-02-06T01:57:14.827Z"},{"error":"Error: Tool Teammate not found\n    at xn_ (/$bunfs/root/claude:1790:5881)\n    at v1 (/$bunfs/root/claude:668:20765)\n    at U6 (/$bunfs/root/claude:668:39157)\n    at Yb (/$bunfs/root/claude:668:49776)\n    at Mx (/$bunfs/root/claude:668:86026)\n    at iT (/$bunfs/root/claude:668:85998)\n    at bdT (/$bunfs/root/claude:668:85840)\n    at dd (/$bunfs/root/claude:668:81240)\n    at nR (/$bunfs/root/…

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