Whenver I open a pdf file in Acrobat Reader (Mac) I have to enter my Adobe account password. Acrobat Reader is a free app, so why do I need to enter the password. This is a pain and will drive me to setting Preview as my default app for viewing pdf documents.
Hope you are doing well and sorry to hear that.
Please go through the help page https://community.adobe.com/t5/acrobat-discussions/acrobat-keeps-asking-to-sign-in/td-p/11525698 and see if that works for you.
Also make sure you have the recent version 22.1.20142 installed. Go to help > Check for updates and reboot the computer once and check if that works for you.
I read the help page you referenced and nothing there made any difference. Also when I looked in my keychain there were five entries for "Adobe.APS"
It's designed to ask, so they can sell you things - that's the reason it's free. However, you don't need to enter it every time - just once, and don't sign out. If this isn't happening, that might be a fixable problem - in fact, that's what the link was about, not the fact that it asks (because it's designed to).