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/server/src/schema.sql

@@ -372,13 +372,12 @@ ALTER TABLE messages ADD COLUMN IF NOT EXISTS tail_start_id UUID REFERENCES mess
 ALTER TABLE chats ADD COLUMN IF NOT EXISTS needs_compaction BOOLEAN NOT NULL DEFAULT FALSE;
 CREATE INDEX IF NOT EXISTS idx_messages_chat_compacted ON messages (chat_id, compacted_at);
 
--- tasks table (provider dispatch, arena)
+-- tasks table (provider dispatch)
 CREATE TABLE IF NOT EXISTS tasks (
   id                UUID PRIMARY KEY DEFAULT gen_random_uuid(),
   project_id        UUID NOT NULL REFERENCES projects(id) ON DELETE CASCADE,
   session_id        UUID REFERENCES sessions(id) ON DELETE CASCADE,
   parent_task_id    UUID REFERENCES tasks(id),
-  arena_id          UUID,
   state             TEXT NOT NULL DEFAULT 'pending'
                     CHECK (state IN ('pending','running','completed','failed','blocked','cancelled')),
   input             TEXT NOT NULL,
@@ -405,3 +404,6 @@ DO $$ BEGIN
       FOREIGN KEY (session_id) REFERENCES sessions(id) ON DELETE CASCADE;
   END IF;
 END $$;
+
+-- Remove the v2.0.5 arena_id column (replaced by the new Arena feature).
+ALTER TABLE tasks DROP COLUMN IF EXISTS arena_id;