@Peter and Everyone. I ran into this exact issue. After spending a few hours befuddled by the nonsense that Android 11 has created with all of this...I decided to take a step back, look at this from a different perspective and had a tada moment :) The best solution sometimes is the most simplistic and one that was right in front of me the whole time. Well, actually, sitting in my laptop bag that's been parked for about a year.
Long story short, I ejected my SD Card, placed it in my previous S9 which was running Android whatever...anything other than Android 11. As soon as I fired it up, checked my Android/Data folder...everything was there, I simply copied it to my Internal Drive, ejected it, returned to the S10 and was back up and running. Thus, I didn't need to Root my device, test over 10+ File Manager Apps, read article after article, etc...I just had to go back in time before Android 11 and I didn't even have to revert my current S10 back to Android 10 or earlier. I just had to take Android 11 out of the picture.
So, while I've seen all of these press releases, specifications, justifications and reasoning for what Android 11 was supposed to do...it just doesn't compute. Never in my 30+ career have I seen a supposedly new solution lead to a 100% non operative solution against a given. In other words, accessing your Android/Data directory was as easy as 1+1, after Android 11 the only number that matters is 0...the number of items you can access :(
I think the moral to the story here is that always having a contingency plan... in this case an older backup phone pays off. I will not bore you with old stories of how my previous phone(s) helped in other situations...but I think today's result sums things up :)
Take care and I hope this helps everyone with this waste of time nonsense. It's OUR data sitting right in front of us that we NEVER had an issue with prior to Android 11.