refactor: Restructure monorepo to apps/server/ and apps/web/ layout

Move src/ → apps/server/ and packages/web/ → apps/web/ to adopt
standard monorepo conventions (apps/ for runnable apps, packages/
for reusable libraries). Update all config files, shared package
imports, test fixtures, and documentation to reflect new paths.

Key fixes:
- Update workspace config to ["apps/*", "packages/*"]
- Update tsconfig.json rootDir/include for apps/server/
- Add apps/web/** to vitest exclude list
- Update drizzle.config.ts schema path
- Fix ensure-schema.ts migration path detection (3 levels up in dev,
  2 levels up in dist)
- Fix tests/integration/cli-server.test.ts import paths
- Update packages/shared imports to apps/server/ paths
- Update all docs/ files with new paths

apps/server/db/repositories/drizzle/agent.ts

@@ -0,0 +1,119 @@
+/**
+ * Drizzle Agent Repository Adapter
+ *
+ * Implements AgentRepository interface using Drizzle ORM.
+ */
+
+import { eq } from 'drizzle-orm';
+import { nanoid } from 'nanoid';
+import type { DrizzleDatabase } from '../../index.js';
+import { agents, type Agent } from '../../schema.js';
+import type {
+  AgentRepository,
+  AgentStatus,
+  CreateAgentData,
+  UpdateAgentData,
+} from '../agent-repository.js';
+
+/**
+ * Drizzle adapter for AgentRepository.
+ *
+ * Uses dependency injection for database instance,
+ * enabling isolated test databases.
+ */
+export class DrizzleAgentRepository implements AgentRepository {
+  constructor(private db: DrizzleDatabase) {}
+
+  async create(data: CreateAgentData): Promise<Agent> {
+    const id = nanoid();
+    const now = new Date();
+
+    const [created] = await this.db.insert(agents).values({
+      id,
+      name: data.name,
+      taskId: data.taskId ?? null,
+      initiativeId: data.initiativeId ?? null,
+      sessionId: data.sessionId ?? null,
+      worktreeId: data.worktreeId,
+      provider: data.provider ?? 'claude',
+      accountId: data.accountId ?? null,
+      status: data.status ?? 'idle',
+      mode: data.mode ?? 'execute',
+      createdAt: now,
+      updatedAt: now,
+    }).returning();
+
+    return created;
+  }
+
+  async findById(id: string): Promise<Agent | null> {
+    const result = await this.db
+      .select()
+      .from(agents)
+      .where(eq(agents.id, id))
+      .limit(1);
+
+    return result[0] ?? null;
+  }
+
+  async findByName(name: string): Promise<Agent | null> {
+    const result = await this.db
+      .select()
+      .from(agents)
+      .where(eq(agents.name, name))
+      .limit(1);
+
+    return result[0] ?? null;
+  }
+
+  async findByTaskId(taskId: string): Promise<Agent | null> {
+    const result = await this.db
+      .select()
+      .from(agents)
+      .where(eq(agents.taskId, taskId))
+      .limit(1);
+
+    return result[0] ?? null;
+  }
+
+  async findBySessionId(sessionId: string): Promise<Agent | null> {
+    const result = await this.db
+      .select()
+      .from(agents)
+      .where(eq(agents.sessionId, sessionId))
+      .limit(1);
+
+    return result[0] ?? null;
+  }
+
+  async findAll(): Promise<Agent[]> {
+    return this.db.select().from(agents);
+  }
+
+  async findByStatus(status: AgentStatus): Promise<Agent[]> {
+    return this.db.select().from(agents).where(eq(agents.status, status));
+  }
+
+  async update(id: string, data: UpdateAgentData): Promise<Agent> {
+    const now = new Date();
+    const [updated] = await this.db
+      .update(agents)
+      .set({ ...data, updatedAt: now })
+      .where(eq(agents.id, id))
+      .returning();
+
+    if (!updated) {
+      throw new Error(`Agent not found: ${id}`);
+    }
+
+    return updated;
+  }
+
+  async delete(id: string): Promise<void> {
+    const [deleted] = await this.db.delete(agents).where(eq(agents.id, id)).returning();
+
+    if (!deleted) {
+      throw new Error(`Agent not found: ${id}`);
+    }
+  }
+}