feat(#4): Implement Authentik OIDC authentication with BetterAuth

- Integrated BetterAuth library for modern authentication
- Added Session, Account, and Verification database tables
- Created complete auth module with service, controller, guards, and decorators
- Implemented shared authentication types in @mosaic/shared package
- Added comprehensive test coverage (26 tests passing)
- Documented type sharing strategy for monorepo
- Updated environment configuration with OIDC and JWT settings

Key architectural decisions:
- BetterAuth over Passport.js for better TypeScript support
- Separation of User (DB entity) vs AuthUser (client-safe subset)
- Shared types package to prevent FE/BE drift
- Factory pattern for auth config to use shared Prisma instance

Ready for frontend integration (Issue #6).

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

Fixes #4

apps/api/src/auth/guards/auth.guard.ts

@@ -0,0 +1,41 @@
+import { Injectable, CanActivate, ExecutionContext, UnauthorizedException } from "@nestjs/common";
+import { AuthService } from "../auth.service";
+
+@Injectable()
+export class AuthGuard implements CanActivate {
+  constructor(private readonly authService: AuthService) {}
+
+  async canActivate(context: ExecutionContext): Promise<boolean> {
+    const request = context.switchToHttp().getRequest();
+    const token = this.extractTokenFromHeader(request);
+
+    if (!token) {
+      throw new UnauthorizedException("No authentication token provided");
+    }
+
+    try {
+      const sessionData = await this.authService.verifySession(token);
+
+      if (!sessionData) {
+        throw new UnauthorizedException("Invalid or expired session");
+      }
+
+      // Attach user to request
+      request.user = sessionData.user;
+      request.session = sessionData.session;
+
+      return true;
+    } catch (error) {
+      // Re-throw if it's already an UnauthorizedException
+      if (error instanceof UnauthorizedException) {
+        throw error;
+      }
+      throw new UnauthorizedException("Authentication failed");
+    }
+  }
+
+  private extractTokenFromHeader(request: any): string | undefined {
+    const [type, token] = request.headers.authorization?.split(" ") ?? [];
+    return type === "Bearer" ? token : undefined;
+  }
+}