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/web/src/api/client.ts

@@ -27,6 +27,9 @@ import type {
   WorkspaceState,
   FlowRunRow,
   FlowStepRow,
+  BattleShape,
+  ContestantShape,
+  CrossExaminationShape,
 } from './types';
 
 // v2.6 Phase 1-UX §9b: chat-scoped agent-session rows. Returned by
@@ -518,6 +521,63 @@ export const api = {
       request<AgentsResponse>(`/api/projects/${projectId}/agents`),
   },
 
+  // Arena battle API — proxied to boocoder at /api/coder/battles/*.
+  battles: {
+    create: (body: {
+      project_id: string;
+      battle_type: 'coding' | 'qa';
+      prompt: string;
+      contestants: Array<{ identity: string; model: string }>;
+    }) =>
+      request<{ battle_id: string }>('/api/coder/battles', {
+        method: 'POST',
+        body: JSON.stringify(body),
+      }),
+    list: (projectId: string) =>
+      request<{ battles: BattleShape[] }>(
+        `/api/coder/battles?project_id=${encodeURIComponent(projectId)}`,
+      ),
+    get: (battleId: string) =>
+      request<{
+        battle: BattleShape;
+        contestants: ContestantShape[];
+        cross_examinations: CrossExaminationShape[];
+      }>(`/api/coder/battles/${encodeURIComponent(battleId)}`),
+    stop: (battleId: string) =>
+      request<{ cancelled: boolean }>(
+        `/api/coder/battles/${encodeURIComponent(battleId)}/stop`,
+        { method: 'POST' },
+      ),
+    analyze: (battleId: string) =>
+      request<{ triggered: boolean }>(
+        `/api/coder/battles/${encodeURIComponent(battleId)}/analyze`,
+        { method: 'POST' },
+      ),
+    crossExamine: (battleId: string, body: { identity: string; model: string }) =>
+      request<{ cross_exam_id: string }>(
+        `/api/coder/battles/${encodeURIComponent(battleId)}/cross-examine`,
+        { method: 'POST', body: JSON.stringify(body) },
+      ),
+    getAnalysis: (battleId: string) =>
+      request<{ text: string }>(
+        `/api/coder/battles/${encodeURIComponent(battleId)}/analysis`,
+      ),
+    generatePrompt: (description: string) =>
+      request<{ prompt: string }>('/api/coder/battles/generate-prompt', {
+        method: 'POST',
+        body: JSON.stringify({ description }),
+      }),
+    setWinner: (battleId: string, body: { winner_contestant_id: string | null }) =>
+      request<{ ok: boolean }>(
+        `/api/coder/battles/${encodeURIComponent(battleId)}/winner`,
+        { method: 'PATCH', body: JSON.stringify(body) },
+      ),
+    getDiff: (battleId: string, contestantId: string) =>
+      request<{ diff: string }>(
+        `/api/coder/battles/${encodeURIComponent(battleId)}/contestants/${encodeURIComponent(contestantId)}/diff`,
+      ),
+  },
+
   skills: {
     list: () => request<{ skills: Skill[] }>('/api/skills'),
   },