feat(web,coder): arena pane — compare 2-6 AI competitors on same prompt

Arena is a new pane kind for competitive AI evaluation. A Battle runs
the same prompt against 2-6 Contestants across two concurrent lanes:
local lane (llama-swap models, serial) and cloud lane (parallel).

Added to all three registries: @boocode/contracts WsFrameSchema,
server InferenceFrame, and web WsFrame.

Backend (apps/coder):
- arena-runner: battle scheduler, lane classifier, benchmark, results
  writer, resume, user winner override
- arena-analyzer: two-stage digest→judge analysis on DEFAULT_MODEL
- arena-decisions: status transitions and resume logic (unit-tested)
- arena-analyzer-helpers: pure helper functions (unit-tested)
- arena-model-call: model call utility for analysis
- arena routes: create/get/list/stop/analyze/cross-examine/winner/diff
- schema: battles, contestants, cross_examinations tables (idempotent)
- remove old /api/arena* routes and tasks.arena_id column

Frontend (apps/web):
- ArenaLauncherDialog: battle type, prompt, contestant selection
- ArenaPane: live roster, streaming output, analysis, cross-exam
- DiffView: unified diff with line-by-line color for coding contests
- Winner override per-row dropdown (Trophy icon)
- battle_updated WS handler for live winner/analysis updates
- arena pane kind in Workspace, ChatTabBar, useSidebar

Cross-app:
- ArenaState and ArenaContestantShape/WsFrame types (contracts)
- battle_* frames in WsFrameSchema, InferenceFrame, and web WsFrame
- manifest.json written per battle results folder
- /Arena added to .gitignore

apps/web/src/hooks/useSidebar.ts

@@ -195,6 +195,13 @@ function applyEvent(prev: SidebarResponse, event: import('./sessionEvents').Sess
     case 'flow_run_step_updated':
       // Consumed by useWorkspacePanes / OrchestratorPane / FlowLauncherDialog; sidebar has no stake.
       return prev;
+    case 'open_arena_launcher':
+    case 'open_arena_pane':
+    case 'battle_started':
+    case 'contestant_updated':
+    case 'battle_updated':
+      // Consumed by useWorkspacePanes / ArenaPane / ArenaLauncherDialog; sidebar has no stake.
+      return prev;
     case 'project_archived': {
       const next = prev.projects.filter((p) => p.id !== event.project_id);
       if (next.length === prev.projects.length) return prev;