Login cookies, yes: by entering the username and password the user is requesting that you log them in.
Shopping carts, sort of: if they don't check out immediately and you keep the item in their cart (which they may want but didn't explicitly request) you're in violation: https://ec.europa.eu/justice/article-29/documentation/opinio...
Other things: it has to be "strictly necessary" which is a high bar and many things don't meet it. For example, implicitly learning your preferences from your behavior doesn't.