Update: I tested and the store() method uses the private key in the local disk array, so I finally found a way to be able to view files locally during development - I add the following permissions block to my local disk:
'local' => [
'driver' => 'local',
'root' => storage_path('uploads'),
'throw' => true,
'permissions' => [
'file' => [
'public' => 0644,
'private' => 0660,
],
'dir' => [
'public' => 0755,
'private' => 0770,
],
],
],