Replace next-auth with Better Auth, migrate DB columns to camelCase

- Replace next-auth v5 beta with better-auth v1.6.2 (stable releases)
- Add multi-provider OAuth support with admin UI configuration
- New oauthProviders table with encrypted secrets (AES-256-GCM)
- Env var bootstrap (OAUTH_*) syncs to DB, UI-created providers fully editable
- OAuth provider REST API: GET/POST/PUT/DELETE /api/v1/oauth-providers
- Settings page "Authentication Providers" section for admin management
- Account linking uses new accounts table (multi-provider per user)
- Username plugin for credentials sign-in (replaces email@localhost pattern)
- bcrypt password compatibility (existing hashes work)
- Database-backed sessions via Kysely adapter (bun:sqlite direct)
- Configurable rate limiting via AUTH_RATE_LIMIT_* env vars
- All DB columns migrated from snake_case to camelCase
- All TypeScript types/models migrated to camelCase properties
- Removed casing: "snake_case" from Drizzle config
- Callback URL format: {baseUrl}/api/auth/oauth2/callback/{providerId}
- package-lock.json removed and gitignored (using bun.lock)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

drizzle/0022_nullable_provider_subject.sql

@@ -0,0 +1,27 @@
+-- Recreate users table for Better Auth compatibility:
+-- 1. provider/subject: nullable with defaults (Better Auth doesn't set these)
+-- 2. emailVerified: INTEGER (matches Better Auth boolean→int conversion)
+CREATE TABLE users_new (
+  id INTEGER PRIMARY KEY AUTOINCREMENT,
+  email TEXT NOT NULL,
+  name TEXT,
+  passwordHash TEXT,
+  role TEXT NOT NULL DEFAULT 'user',
+  provider TEXT DEFAULT '',
+  subject TEXT DEFAULT '',
+  avatarUrl TEXT,
+  status TEXT NOT NULL DEFAULT 'active',
+  username TEXT,
+  displayUsername TEXT,
+  emailVerified INTEGER NOT NULL DEFAULT 0,
+  createdAt TEXT NOT NULL,
+  updatedAt TEXT NOT NULL
+);
+--> statement-breakpoint
+INSERT INTO users_new SELECT id, email, name, passwordHash, role, provider, subject, avatarUrl, status, username, displayUsername, emailVerified, createdAt, updatedAt FROM users;
+--> statement-breakpoint
+DROP TABLE users;
+--> statement-breakpoint
+ALTER TABLE users_new RENAME TO users;
+--> statement-breakpoint
+CREATE UNIQUE INDEX users_email_unique ON users (email);