fix(tui): address Copilot review on #14045

Four real issues Copilot flagged:

1. delegate_tool: `_build_child_agent` never passed `toolsets` to the
   progress callback, so the event payload's `toolsets` field (wired
   through every layer) was always empty and the overlay's toolsets
   row never populated.  Thread `child_toolsets` through.

2. event handler: the race-protection on subagent.spawn_requested /
   subagent.start only preserved `completed`, so a late-arriving queued
   event could clobber `failed` / `interrupted` too.  Preserve any
   terminal status (`completed | failed | interrupted`).

3. SpawnHud: comment claimed concurrency was approximated by "widest
   level in the tree" but code used `totals.activeCount` (total across
   all parents).  `max_concurrent_children` is a per-parent cap, so
   activeCount over-warns for multi-orchestrator runs.  Switch to
   `max(widthByDepth(tree))`; the label now reads `⚡W/cap+extra` where
   W is the widest level (drives the ratio) and `+extra` is the rest.

4. spawn_tree.list: comment said "peek header without parsing full list"
   but the code json.loads()'d every snapshot.  Adds a per-session
   `_index.jsonl` sidecar written on save; list() reads only the index
   (with a full-scan fallback for pre-index sessions).  O(1) per
   snapshot now vs O(file-size).

tools/delegate_tool.py

@@ -849,6 +849,7 @@ def _build_child_agent(
         parent_id=parent_subagent_id,
         depth=tui_depth,
         model=effective_model_for_cb,
+        toolsets=child_toolsets,
     )
 
     # Each subagent gets its own iteration budget capped at max_iterations