Steps to reproduce the issue

As soon as I try to load the Endpoint /api/index.php/v1/users, the repsonse is "Unable to load router: api".

Expected result

JRouterApi should be alias for ApiRouter, like SiteRouter and AdministratorRouter.

$container->alias('AdministratorRouter', AdministratorRouter::class)
            ->alias('JRouterAdministrator', AdministratorRouter::class)

$container->alias('SiteRouter', SiteRouter::class)
            ->alias('JRouterSite', SiteRouter::class)

Actual result

JRouterApi is no alias for ApiRouter.

$container->alias('ApiRouter', ApiRouter::class)
            ->share(
                ApiRouter::class,
                function (Container $container) {
                    return new ApiRouter($container->get(ApiApplication::class));
                },
                true
            );

So the Joomla\CMS\Router\Router class will fail at:

$classname = 'JRouter' . ucfirst($client);

if (!class_exists($classname)) {
    throw new \RuntimeException(Text::sprintf('JLIB_APPLICATION_ERROR_ROUTER_LOAD', $client), 500);
}

System information (as much as possible)

Joomla 4.4.8, PHP 8.1.29, Apache Server