I think that browser protection (previously called password protection, see my screenshot on a non-updated PC) is different from password manager.
As far as I'm concerned, on the PC where I did the update, I don't use the avast password manager, but I use the new browser protection (cookie and password policy) as used before without the coockies protection.
In any case, I don't have any logon issue every time I re-open my browser.
If you have a problem, it may not be related to the new function, or it may be related to password manager.
By any chance, have you tried to repair avast?