Add session groups with broadcast-input support

[AThraen]

Generated from a competitor-analysis pass (TerminalConductor, May 2026).

Summary

Let users tag sessions into named groups and toggle a broadcast mode where keystrokes typed into the active session are mirrored to every other session in the group.

Motivation

Classic multi-terminal use cases we currently lack:

• "Kick off npm test in all three services at once."
• "Restart all the agents."
• "Send the same prompt to Claude + Codex side-by-side for comparison."
• "Apply the same git pull across all worktrees."

tmux has it. Windows Terminal has it. TerminalConductor has it. We have SessionGroup as a model already but no real grouping or broadcast wired up.

Proposed behaviour

Data model

• Extend SessionGroup (already in Models/SessionGroup.cs): Id, Name, Color, SessionIds: List<string>.
• AppState.Groups: List<SessionGroup> persisted to state.json.
• Sessions can belong to at most one group (start simple — multi-group later if needed).

Sidebar UI

• Group header row above its member sessions; collapsible with ▼/▶.
• Member sessions get a 2px left border in the group color (in addition to their own accent stripe).
• Right-click a session → "Add to group…" submenu (existing groups or "New group…").
• Right-click a group header → Rename / Change color / Broadcast input / Delete group.

Broadcast mode

• Toggle per-group, NOT persisted across runs (deliberate — broadcast is a deliberate action).
• When ON, a banner appears above the active terminal: "Broadcasting to '' (3 sessions)" with a [Stop broadcast] button.
• Mechanism: hook in TerminalBridge.WriteInput — for the active session, also forward to each other group member's bridge.
• Member tabs get a distinct 2px outer ring in the group color (using the same active-ring border the active session uses, but recoloured to the group accent).

Safety

• Broadcast OFF automatically when:
  • Active session leaves the group
  • The group is deleted
  • App closes (state not persisted)
• Each session receives keystrokes individually; \r is NOT auto-injected. User presses Enter once, every group member receives that Enter.

Out of scope

• Conditional broadcast (different command per host) — broadcast = exact same bytes.
• Multi-group membership.
• Per-session opt-out within a broadcast (just remove from the group).

Inspiration

TerminalConductor's "Group broadcast" + manual groups. See https://terminalconductor.com/.