Phase 2.1 — Open investigations in named tmux windows instead of splitting the TUI pane

[ooloth]

Phase 2.1 of #327. The title numbering is the work order: take milestone issues in Phase N.M order. The one hard dependency is #331 on #330, recorded as blockedBy; the rest is sequence, not blocking. Read gh issue view 327 --comments for the plan of record.

Current state

Launching more than one or two investigations crowds the TUI out of the viewport, and no investigation is addressable afterwards. ui/tui/src/investigations/launch.rs:110 runs tmux split-window -h -t $TMUX_PANE, so every investigation subdivides the TUI's own pane and none of them carries a name. The same file already uses tmux new-window -n <name> for open_in_lazygit (line 150) and open_in_octo (line 186), with the name built from repo and PR number, so the pattern exists but the investigation path does not use it.

#54 previously fixed which pane the split targets. Moving to a named window supersedes that mechanism rather than regressing it.

Ideal state

• Pressing i opens the investigation in its own tmux window rather than a split of the TUI's pane
• The window name is derived deterministically from the signal, so the same item always produces the same name
• The TUI keeps its full window when an investigation launches
• Several investigations run at once, each in its own named window, reachable from tmux's window list
• Launching outside tmux still fails with the existing clear message

Out of scope

• Refusing to open a second window for an item that already has one — that is the next issue in this phase, and it depends on the names this one introduces
• Prompt content, model selection, and allowed tools, which are unchanged
• Worktree resolution, which is unchanged

Starting points

• ui/tui/src/investigations/launch.rs — launch() at line 64, and the new-window naming already used by open_in_lazygit at line 150
• ui/tui/src/investigations/mod.rs — the module doc describes the split-window behavior and needs to change with it

QA plan

1. Start the TUI in tmux, select a PR, press i — expect a new tmux window rather than a split, with the TUI still occupying its full window
2. Run tmux list-windows — expect a window whose name identifies that PR by repo and number
3. Return to the TUI, select a different PR, press i — expect a second, separately named window, with the TUI still full-size
4. Switch into one of the investigation windows — expect a running Claude Code session with the same prompt it received before this change
5. Run the TUI outside tmux and press i — expect the existing "not in tmux" error rather than a panic

Done when

Pressing i opens a deterministically named tmux window instead of splitting the TUI's pane.