Sbenny, I think you need "Root Access" to get the .obb files into the "obb" folder. That's what I found so far in Android 11 or above.
Sadly, I do not have a root access phone so which means the other file managers might do the same (not allowing .obb files moved to "obb" folder).
I tried "Explorer" but it seems like it's doing the same thing, not allowing. And I also tried moving the .obb files into obb folder through my Laptop but it's also not allowing.
If you have any other solution for this issue, I'd like to hear and try.