feat: establish core identity foundation

Adds Core-owned identity contracts, a Core-owned Better Auth database schema
(ekklesia_core_user/session/account/verification), a first-class Core-owned
migration source that coexists with module-owned migrations under the exact
existing migration system, and an explicit Better Auth construction boundary.
No authentication endpoint or sign-in UI is exposed yet (ADR 0010).

Co-Authored-By: Claude Sonnet 5 <[email protected]>

core/tests/identity-database.test.ts

@@ -0,0 +1,67 @@
+import { describe, expect, it, vi } from "vitest";
+
+const poolConstructor = vi.hoisted(() => vi.fn());
+
+vi.mock("pg", () => ({ Pool: poolConstructor }));
+
+import { createIdentityDrizzleDatabase, IdentityDatabaseError } from "../src/identity/database.js";
+
+describe("Core identity Drizzle database composition", () => {
+  it("does not construct a pool merely because the module is imported", () => {
+    expect(poolConstructor).not.toHaveBeenCalled();
+  });
+
+  it.each([
+    "",
+    "   ",
+    "not-a-database-url",
+    "https://admin:[email protected]/database",
+  ])("rejects an invalid connection string without exposing it (%s)", (connectionString) => {
+    let captured: unknown;
+    try {
+      createIdentityDrizzleDatabase(connectionString);
+    } catch (error) {
+      captured = error;
+    }
+
+    expect(captured).toBeInstanceOf(IdentityDatabaseError);
+    expect(captured).toMatchObject({ code: "IDENTITY_DATABASE_CONFIGURATION_INVALID" });
+    const publicText = `${String(captured)}\n${
+      captured instanceof Error ? (captured.stack ?? "") : ""
+    }`;
+    if (connectionString) {
+      expect(publicText).not.toContain(connectionString);
+    }
+    expect(poolConstructor).not.toHaveBeenCalled();
+  });
+
+  it("explicitly constructs the pool only when called, with the identity schema attached", () => {
+    poolConstructor.mockImplementation(function fakePool() {
+      return { end: async () => undefined };
+    });
+
+    const handle = createIdentityDrizzleDatabase(
+      "postgresql://operator:[email protected]/ekklesia",
+    );
+
+    expect(poolConstructor).toHaveBeenCalledTimes(1);
+    expect(handle.db).toBeDefined();
+    expect(typeof handle.close).toBe("function");
+    expect(Object.isFrozen(handle)).toBe(true);
+  });
+
+  it("passes the connection timeout through to the pool configuration", () => {
+    poolConstructor.mockImplementation(function fakePool() {
+      return { end: async () => undefined };
+    });
+    poolConstructor.mockClear();
+
+    createIdentityDrizzleDatabase("postgresql://example.test/ekklesia", {
+      connectionTimeoutMs: 5_000,
+    });
+
+    expect(poolConstructor).toHaveBeenCalledWith(
+      expect.objectContaining({ connectionTimeoutMillis: 5_000 }),
+    );
+  });
+});