Your first route

Routes are registered in one place, by a provider:

use Quillstack\Framework\Interfaces\RouteProviderInterface;
use Quillstack\Router\Router;

final class RouteProvider implements RouteProviderInterface
{
    public function setRoutes(Router $router): void
    {
        $router->get('/', HomeController::class)->name('home');
        $router->get('/users/:id', UserController::class)->name('users.show');
        $router->delete('/users/{id}', DeleteUserController::class);
    }
}

get(), post(), put(), patch(), delete(), options() and head() register a single method. match(['PUT', 'PATCH'], …) registers several, and any() registers them all.

Parameters

A segment written :id or {id} is a parameter. What matched is put on the request as an attribute, and a query string never takes part in the matching:

use Psr\Http\Message\ServerRequestInterface;
use Quillstack\Framework\Interfaces\ControllerInterface;

final class UserController implements ControllerInterface
{
    public function __construct(private readonly UserResponse $response)
    {
    }

    public function handle(ServerRequestInterface $request): UserResponse
    {
        $id = $request->getAttribute('id');

        // An attribute is whatever was put there, so it is worth asking what it is
        // before using it.
        if (!is_string($id)) {
            throw new NotFoundHttpException('No such user');
        }

        return $this->response->with($this->users->find((int) $id));
    }
}

The controller is asked for by name, so the container builds it with whatever its constructor declares — see The container.

When nothing matches

A path nobody registered is answered 404. A path registered for a different method is answered 405, and the response names the methods that path does answer to — the difference between there is no such thing and not that way.

HEAD is answered by whatever answers GET, with the headers and no body, unless a head() route was registered for it.

Errors

Nothing thrown by the application reaches the client as a fatal error. An HTTP exception is answered with the status it carries:

use Quillstack\Framework\Exceptions\Http\NotFoundHttpException;

throw new NotFoundHttpException('No user with that id');

Anything else is a 500, logged in full and described to the client only as far as the environment allows.

More: Router, Middleware.