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

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

apps/server/src/services/inference/types.ts

@@ -44,7 +44,11 @@ export interface InferenceFrame {
     | 'chat_renamed'
     | 'error'
     | 'flow_run_started'
-    | 'flow_run_step_updated';
+    | 'flow_run_step_updated'
+    // arena frames
+    | 'battle_started'
+    | 'contestant_updated'
+    | 'battle_updated';
   message_id?: string;
   message_ids?: string[];
   chat_id?: string;
@@ -84,6 +88,19 @@ export interface InferenceFrame {
   status?: string;
   run_status?: 'running' | 'completed' | 'failed' | 'cancelled';
   report?: string;
+  // arena frames
+  battle_id?: string;
+  battle_type?: 'coding' | 'qa';
+  prompt?: string;
+  contestants?: Array<{ id: string; identity: string; model: string; lane: 'local' | 'cloud' }>;
+  contestant_id?: string;
+  battle_status?: 'pending' | 'running' | 'completed' | 'failed' | 'cancelled';
+  duration_ms?: number;
+  tokens_per_sec?: number;
+  winner_contestant_id?: string | null;
+  analysis_ready?: boolean;
+  cross_exam_id?: string;
+  delta?: string;
 }
 
 export type FramePublisher = (sessionId: string, frame: InferenceFrame) => void;