In their document maybe you should see,

// Laravel 9 uses $routeMiddleware = [
//protected $routeMiddleware = [
// Laravel 10  uses $middlewareAliases = [
protected $middlewareAliases = [
    // ...
    'role' => \Spatie\Permission\Middleware\RoleMiddleware::class,
    'permission' => \Spatie\Permission\Middleware\PermissionMiddleware::class,
    'role_or_permission' => \Spatie\Permission\Middleware\RoleOrPermissionMiddleware::class,
];

But it would be

// Laravel 9 uses $routeMiddleware = [
//protected $routeMiddleware = [
// Laravel 10  uses $middlewareAliases = [
protected $middlewareAliases = [
    // ...
    'role' => \Spatie\Permission\Middlewares\RoleMiddleware::class,
    'permission' => \Spatie\Permission\Middlewares\PermissionMiddleware::class,
    'role_or_permission' => \Spatie\Permission\Middlewares\RoleOrPermissionMiddleware::class,
];

Just add extra 's' there. 

'permission' => \Spatie\Permission\Middlewares\PermissionMiddleware::class,