I too am having the same problem! I have gone through the tutorial here,.....
https://support.avast.com/en-ww/article/Synchronize-Passwords-across-devices/....but when I get to the part where I want to turn Sync "on" the next window asks me to log in
Can't log in!!!
I try logging in using the Google option. Doesn't work!!!
I have a Android phone and an iPad with all my Passwords so it should be a 5 minute process to get my PC Avast working. So I spent One day reinstalling W10 to fix one major issue, only to spend the better part of another just trying to get Avast Passwords to work. Very frustrating as I to am a paying customer.
Edit:
So I've been at this all day again. As to the ability to log in so that I can Sync my passwords, I was able to get to the "type the letters & numbers but alas it just gave me the same old error. "we have run into a problem and cannot log you in"
Well !!!
Pretty pissed off at this point !