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/useCoderUserEvents.ts

@@ -8,7 +8,13 @@
 import { useEffect } from 'react';
 import { WsFrameSchema } from '@boocode/contracts/ws-frames';
 import { sessionEvents } from './sessionEvents';
-import type { FlowRunStartedEvent, FlowRunStepUpdatedEvent } from './sessionEvents';
+import type {
+  BattleStartedEvent,
+  BattleUpdatedEvent,
+  ContestantUpdatedEvent,
+  FlowRunStartedEvent,
+  FlowRunStepUpdatedEvent,
+} from './sessionEvents';
 
 const RECONNECT_INITIAL_MS = 1000;
 const RECONNECT_MAX_MS = 30_000;
@@ -49,6 +55,12 @@ export function useCoderUserEvents(): void {
           sessionEvents.emit(frame as unknown as FlowRunStartedEvent);
         } else if (frame.type === 'flow_run_step_updated') {
           sessionEvents.emit(frame as unknown as FlowRunStepUpdatedEvent);
+        } else if (frame.type === 'battle_started') {
+          sessionEvents.emit(frame as unknown as BattleStartedEvent);
+        } else if (frame.type === 'contestant_updated') {
+          sessionEvents.emit(frame as unknown as ContestantUpdatedEvent);
+        } else if (frame.type === 'battle_updated') {
+          sessionEvents.emit(frame as unknown as BattleUpdatedEvent);
         }
       };