So, after spending fair amount of time with 625 different file managers I found out that this just does not work. Even the apps that ask for permission can't get one because we are never presented with this or something like this

but file commander and other show this as a helper

but it leads to nowhere because the chooser from above never opens. There's no way to grant permission, it always end with some error. And the only meaningful one is from x-plorer that tells me this :

"no activity found to handle intent {act=android.intent.action.open_document_tree (has extras)}"