feat: Claude Agent SDK backend + clean-room PostgresSessionStore (v2.7.5)

Lands the lean-SDK direction (boocode_code_review_v2 §1 #9) behind a flag.
Adds @anthropic-ai/claude-agent-sdk@0.3.159 (Commercial Terms, runtime dep).

- PostgresSessionStore: clean-room impl of the SDK's real SessionStore type
  over a new claude_session_entries table. Typechecks against the SDK type;
  8 DB-integration tests.
- ClaudeSdkBackend (implements AgentBackend): one warm query() per (chat,claude)
  in streaming-input mode via a pushable async-iterable pump, sessionStore +
  resume continuity, pure mapSdkMessage->AgentEvent, session_id from init,
  usage/cost onto agent_sessions (backend CHECK gains 'claude_sdk').
- Routing env-gated by CLAUDE_SDK_BACKEND (default off) -> PTY path UNCHANGED.
- Built against real SDK 0.3.159 types (install paid off: partial=stream_event
  needing includePartialMessages, MessageParam, result error arm).
- Fix latent test-infra deadlock: serialize DB suites (fileParallelism:false).

Coder 269 passing default / 290 with DB; tsc clean vs SDK types; builds clean.
LIVE pump + resume + actual claude turn need a host smoke (CLAUDE_SDK_BACKEND=1
+ claude binary + auth). zod peer-dep wants ^4 (workspace 3.25). Builds on v2.7.4.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

apps/coder/src/services/backends/claude-sdk-routing.ts

@@ -0,0 +1,38 @@
+/**
+ * claude-sdk-sessionstore #9 (Part 2) — claude-SDK-vs-PTY routing predicate.
+ *
+ * Sibling to `shouldUseWarmBackend` (warm-acp-routing.ts). The warm Claude-SDK
+ * backend keys its persistent `query()` on (chat_id, agent) — exactly like the
+ * warm-ACP / opencode-server backends — so a task only routes to it when it carries
+ * BOTH a `session_id` and a `chat_id` (a real chat tab).
+ *
+ * CRUCIALLY this is ALSO gated behind the `CLAUDE_SDK_BACKEND` env flag (default
+ * OFF). While off — the production default — claude always falls through to the
+ * existing one-shot PTY `runExternalAgent` path, UNCHANGED. The live SDK streaming
+ * pump + cross-turn resume need a host smoke against the real `claude` binary, so
+ * we keep the working PTY path as the default until that lands. Flip the env var
+ * on a host (any truthy value) to opt a deployment into the SDK backend.
+ *
+ * Pure (env read injected) so it's unit-testable; the dispatcher consumes it.
+ */
+
+/** True iff the `CLAUDE_SDK_BACKEND` env flag is set to a truthy value. */
+export function claudeSdkBackendEnabled(env: NodeJS.ProcessEnv = process.env): boolean {
+  const v = env.CLAUDE_SDK_BACKEND;
+  if (v == null) return false;
+  const s = v.trim().toLowerCase();
+  return s !== '' && s !== '0' && s !== 'false' && s !== 'off' && s !== 'no';
+}
+
+export function shouldUseClaudeSdk(
+  task: {
+    agent: string | null;
+    session_id: string | null;
+    chat_id: string | null;
+  },
+  env: NodeJS.ProcessEnv = process.env,
+): boolean {
+  if (!claudeSdkBackendEnabled(env)) return false;
+  if (task.agent !== 'claude') return false;
+  return task.session_id != null && task.chat_id != null;
+}