@leocg OK, I need to make a correction. Looks like Opera Beta is still the only Opera browser on my PC. I confused this with Opera Stable because when I keep my mouse on the symbol on the task bar to see its name, only "Opera" was appearing. Then I checked the actual shortcut and saw "Opera Beta".
However, the remaining problems are the same. I believe that the browser were actually removed and reinstalled during the update because after the update (along with all other issues) its symbol removed from the task bar (it was pinned) and it was no longer the default browser on my PC.
So, the profile folder for Opera Beta is still on my PC.