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/App.tsx

@@ -16,6 +16,7 @@ import { RightRailDrawerProvider, useRightRailDrawer } from '@/hooks/useRightRai
 import { useViewport } from '@/hooks/useViewport';
 import { ThemeFx } from '@/components/fx/ThemeFx';
 import { FlowLauncherDialog } from '@/components/FlowLauncherDialog';
+import { ArenaLauncherDialog } from '@/components/ArenaLauncherDialog';
 
 function SessionRightRail() {
   const { id } = useParams<{ id: string }>();
@@ -102,6 +103,7 @@ function AppShell() {
         </Routes>
         <Toaster position="bottom-right" />
         <FlowLauncherDialog />
+        <ArenaLauncherDialog />
       </div>
     </>
   );