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

docs/adr/0002-arena-dedicated-tables-not-flow-runner.md

@@ -0,0 +1,22 @@
+# Arena gets dedicated battles/contestants tables and replaces the old API-only arena
+
+The Arena feature reuses the dispatcher, the `onTaskTerminal` advance hook, the
+streaming→WS-frame pipeline, and the pane pattern from the Orchestrator, but
+persists to its **own `battles` + `contestants` tables** rather than the
+Orchestrator's `flow_runs`/`flow_steps`. A Battle is not shaped like a flow — it
+has two scheduling lanes, per-contestant benchmarks, on-disk results folders, a
+two-stage analysis, and cross-examinations — so modelling it as flow steps would
+fight the schema. Each Contestant links to a real `tasks` row via `task_id`,
+inheriting all worktree/streaming/dispatch machinery. This also **replaces the
+earlier v2.0.5 API-only arena** (`POST /api/arena`, `tasks.arena_id`,
+select-winner): that feature had no UI and no users, and the new Arena is a
+strict superset, so the old routes and the `tasks.arena_id` column are removed
+rather than left as a second, competing "arena" concept.
+
+## Consequences
+
+- Analysis and cross-examination run through a small pluggable **Analyzer** seam
+  (v1 = default-model two-stage judge). A v2 that drives a Han Orchestrator flow
+  as the analyzer slots in behind that seam without a schema change.
+- The `arena` pane kind, `ArenaState`, and `battle_*` WS frames are added
+  alongside (not folded into) the Orchestrator's, mirroring its patterns.