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/__tests__/claude-sdk-routing.test.ts

@@ -0,0 +1,49 @@
+import { describe, it, expect } from 'vitest';
+import { shouldUseClaudeSdk, claudeSdkBackendEnabled } from '../claude-sdk-routing.js';
+
+/**
+ * Env-flagged routing for the warm Claude-SDK backend. With CLAUDE_SDK_BACKEND off
+ * (the production default) every claude task falls through to the unchanged PTY path;
+ * with it on, only chat-tab claude tasks (session_id + chat_id) route to the SDK.
+ */
+const ON = { CLAUDE_SDK_BACKEND: '1' } as NodeJS.ProcessEnv;
+const OFF = {} as NodeJS.ProcessEnv;
+
+describe('claudeSdkBackendEnabled', () => {
+  it('is false when unset or falsy', () => {
+    expect(claudeSdkBackendEnabled({} as NodeJS.ProcessEnv)).toBe(false);
+    expect(claudeSdkBackendEnabled({ CLAUDE_SDK_BACKEND: '' } as NodeJS.ProcessEnv)).toBe(false);
+    expect(claudeSdkBackendEnabled({ CLAUDE_SDK_BACKEND: '0' } as NodeJS.ProcessEnv)).toBe(false);
+    expect(claudeSdkBackendEnabled({ CLAUDE_SDK_BACKEND: 'false' } as NodeJS.ProcessEnv)).toBe(false);
+    expect(claudeSdkBackendEnabled({ CLAUDE_SDK_BACKEND: 'off' } as NodeJS.ProcessEnv)).toBe(false);
+    expect(claudeSdkBackendEnabled({ CLAUDE_SDK_BACKEND: 'no' } as NodeJS.ProcessEnv)).toBe(false);
+  });
+
+  it('is true for any other truthy value', () => {
+    expect(claudeSdkBackendEnabled({ CLAUDE_SDK_BACKEND: '1' } as NodeJS.ProcessEnv)).toBe(true);
+    expect(claudeSdkBackendEnabled({ CLAUDE_SDK_BACKEND: 'true' } as NodeJS.ProcessEnv)).toBe(true);
+    expect(claudeSdkBackendEnabled({ CLAUDE_SDK_BACKEND: 'on' } as NodeJS.ProcessEnv)).toBe(true);
+  });
+});
+
+describe('shouldUseClaudeSdk', () => {
+  it('is always false while the env flag is off — production claude stays on PTY', () => {
+    expect(shouldUseClaudeSdk({ agent: 'claude', session_id: 's1', chat_id: 'c1' }, OFF)).toBe(false);
+  });
+
+  it('routes a chat-tab claude task to the SDK when the flag is on', () => {
+    expect(shouldUseClaudeSdk({ agent: 'claude', session_id: 's1', chat_id: 'c1' }, ON)).toBe(true);
+  });
+
+  it('only applies to the claude agent', () => {
+    expect(shouldUseClaudeSdk({ agent: 'qwen', session_id: 's1', chat_id: 'c1' }, ON)).toBe(false);
+    expect(shouldUseClaudeSdk({ agent: 'opencode', session_id: 's1', chat_id: 'c1' }, ON)).toBe(false);
+    expect(shouldUseClaudeSdk({ agent: null, session_id: 's1', chat_id: 'c1' }, ON)).toBe(false);
+  });
+
+  it('requires both session_id and chat_id (session-less creators stay one-shot)', () => {
+    expect(shouldUseClaudeSdk({ agent: 'claude', session_id: null, chat_id: null }, ON)).toBe(false);
+    expect(shouldUseClaudeSdk({ agent: 'claude', session_id: 's1', chat_id: null }, ON)).toBe(false);
+    expect(shouldUseClaudeSdk({ agent: 'claude', session_id: null, chat_id: 'c1' }, ON)).toBe(false);
+  });
+});