fix(api): reconcile better-auth schema with installed better-auth CLI output

The Task 3 schema drifted from what better-auth@1.6.18's CLI generates: it used
mode:'timestamp' (epoch seconds) instead of 'timestamp_ms', left verification
timestamps nullable, and omitted the default expressions and helper indexes.

Regenerated src/db/schema.ts from `@better-auth/cli generate` (authoritative per
the plan's version-drift rule) and rebuilt migration 0000 from scratch (no data
exists yet). Converted the index callbacks from the CLI's array form to the
object form required by drizzle-orm@0.36.4's types. Adds session_userId_idx,
account_userId_idx, verification_identifier_idx and the unixepoch defaults.

Tests (health, db, auth sign-up/sign-in, /api/me round-trip) all pass; typecheck
clean; db:generate reports no pending changes.

apps/api/src/db/schema.ts

@@ -1,51 +1,111 @@
-import { sqliteTable, text, integer } from 'drizzle-orm/sqlite-core';
+import { relations, sql } from 'drizzle-orm';
+import { sqliteTable, text, integer, index } from 'drizzle-orm/sqlite-core';
+
+// better-auth core tables. This schema is generated by the better-auth CLI
+// (`npx @better-auth/cli generate --config src/auth.ts`) and is the AUTHORITATIVE
+// shape for the installed better-auth version — do not hand-edit; regenerate instead.
 
 export const user = sqliteTable('user', {
   id: text('id').primaryKey(),
   name: text('name').notNull(),
   email: text('email').notNull().unique(),
-  emailVerified: integer('email_verified', { mode: 'boolean' }).notNull().default(false),
+  emailVerified: integer('email_verified', { mode: 'boolean' }).default(false).notNull(),
   image: text('image'),
-  createdAt: integer('created_at', { mode: 'timestamp' }).notNull(),
-  updatedAt: integer('updated_at', { mode: 'timestamp' }).notNull(),
+  createdAt: integer('created_at', { mode: 'timestamp_ms' })
+    .default(sql`(cast(unixepoch('subsecond') * 1000 as integer))`)
+    .notNull(),
+  updatedAt: integer('updated_at', { mode: 'timestamp_ms' })
+    .default(sql`(cast(unixepoch('subsecond') * 1000 as integer))`)
+    .$onUpdate(() => new Date())
+    .notNull(),
 });
 
-export const session = sqliteTable('session', {
-  id: text('id').primaryKey(),
-  expiresAt: integer('expires_at', { mode: 'timestamp' }).notNull(),
-  token: text('token').notNull().unique(),
-  createdAt: integer('created_at', { mode: 'timestamp' }).notNull(),
-  updatedAt: integer('updated_at', { mode: 'timestamp' }).notNull(),
-  ipAddress: text('ip_address'),
-  userAgent: text('user_agent'),
-  userId: text('user_id')
-    .notNull()
-    .references(() => user.id, { onDelete: 'cascade' }),
-});
+export const session = sqliteTable(
+  'session',
+  {
+    id: text('id').primaryKey(),
+    expiresAt: integer('expires_at', { mode: 'timestamp_ms' }).notNull(),
+    token: text('token').notNull().unique(),
+    createdAt: integer('created_at', { mode: 'timestamp_ms' })
+      .default(sql`(cast(unixepoch('subsecond') * 1000 as integer))`)
+      .notNull(),
+    updatedAt: integer('updated_at', { mode: 'timestamp_ms' })
+      .$onUpdate(() => new Date())
+      .notNull(),
+    ipAddress: text('ip_address'),
+    userAgent: text('user_agent'),
+    userId: text('user_id')
+      .notNull()
+      .references(() => user.id, { onDelete: 'cascade' }),
+  },
+  (table) => ({
+    sessionUserIdIdx: index('session_userId_idx').on(table.userId),
+  })
+);
 
-export const account = sqliteTable('account', {
-  id: text('id').primaryKey(),
-  accountId: text('account_id').notNull(),
-  providerId: text('provider_id').notNull(),
-  userId: text('user_id')
-    .notNull()
-    .references(() => user.id, { onDelete: 'cascade' }),
-  accessToken: text('access_token'),
-  refreshToken: text('refresh_token'),
-  idToken: text('id_token'),
-  accessTokenExpiresAt: integer('access_token_expires_at', { mode: 'timestamp' }),
-  refreshTokenExpiresAt: integer('refresh_token_expires_at', { mode: 'timestamp' }),
-  scope: text('scope'),
-  password: text('password'),
-  createdAt: integer('created_at', { mode: 'timestamp' }).notNull(),
-  updatedAt: integer('updated_at', { mode: 'timestamp' }).notNull(),
-});
+export const account = sqliteTable(
+  'account',
+  {
+    id: text('id').primaryKey(),
+    accountId: text('account_id').notNull(),
+    providerId: text('provider_id').notNull(),
+    userId: text('user_id')
+      .notNull()
+      .references(() => user.id, { onDelete: 'cascade' }),
+    accessToken: text('access_token'),
+    refreshToken: text('refresh_token'),
+    idToken: text('id_token'),
+    accessTokenExpiresAt: integer('access_token_expires_at', { mode: 'timestamp_ms' }),
+    refreshTokenExpiresAt: integer('refresh_token_expires_at', { mode: 'timestamp_ms' }),
+    scope: text('scope'),
+    password: text('password'),
+    createdAt: integer('created_at', { mode: 'timestamp_ms' })
+      .default(sql`(cast(unixepoch('subsecond') * 1000 as integer))`)
+      .notNull(),
+    updatedAt: integer('updated_at', { mode: 'timestamp_ms' })
+      .$onUpdate(() => new Date())
+      .notNull(),
+  },
+  (table) => ({
+    accountUserIdIdx: index('account_userId_idx').on(table.userId),
+  })
+);
 
-export const verification = sqliteTable('verification', {
-  id: text('id').primaryKey(),
-  identifier: text('identifier').notNull(),
-  value: text('value').notNull(),
-  expiresAt: integer('expires_at', { mode: 'timestamp' }).notNull(),
-  createdAt: integer('created_at', { mode: 'timestamp' }),
-  updatedAt: integer('updated_at', { mode: 'timestamp' }),
-});
+export const verification = sqliteTable(
+  'verification',
+  {
+    id: text('id').primaryKey(),
+    identifier: text('identifier').notNull(),
+    value: text('value').notNull(),
+    expiresAt: integer('expires_at', { mode: 'timestamp_ms' }).notNull(),
+    createdAt: integer('created_at', { mode: 'timestamp_ms' })
+      .default(sql`(cast(unixepoch('subsecond') * 1000 as integer))`)
+      .notNull(),
+    updatedAt: integer('updated_at', { mode: 'timestamp_ms' })
+      .default(sql`(cast(unixepoch('subsecond') * 1000 as integer))`)
+      .$onUpdate(() => new Date())
+      .notNull(),
+  },
+  (table) => ({
+    verificationIdentifierIdx: index('verification_identifier_idx').on(table.identifier),
+  })
+);
+
+export const userRelations = relations(user, ({ many }) => ({
+  sessions: many(session),
+  accounts: many(account),
+}));
+
+export const sessionRelations = relations(session, ({ one }) => ({
+  user: one(user, {
+    fields: [session.userId],
+    references: [user.id],
+  }),
+}));
+
+export const accountRelations = relations(account, ({ one }) => ({
+  user: one(user, {
+    fields: [account.userId],
+    references: [user.id],
+  }),
+}));