Just got the new beta update on Xbox 1 (1.16.210.57) the issues is fixed for me
I have the same issue currently happening. I did split screen and my player 2 also can mine but won't pick up anything. Yet player 1 shows the block wasn't mined. All permissions are were they should be. I tried making the game not multi-player and still have the issue. Tried different accounts and still have the issue. Didn't have this issue until the last update for beta (1.16.210.56) i am on Xbox 1.
Just got the new beta update for Xbox 1. (1.16.210.57) the issue is still there.