I had the same problem. It turned out that the adblock app I was using (Blockada) blocked Samsung account app or something. I was able to login again after disconnecting Blockada
S8+ on Pie
First you must go to-
Settings/ Lock Screen/ Secure Lock Settings/ then disable "Local Network And Security" otherwise you won't get your verification code.
I've been getting the "Processing Error" message over the last 2 days.
After changing my password again and again, and still getting that message, I stopped changing my password.
I've tried to sign in all day long and still couldn't log in.
I went to
Selected 1:1 enquiry, signed in there, and it worked first time. After that I went to Galaxy Play Store, signed in there. When I went to my Samsung account it was already logged in.