Fun fact: if you have user accounts, the act of logging in is literally the act that consents to storing and handling PII (unless you're so bad at writing a signup agreement that you forgot to put that in there).

If you don't require users to be logged in to serve content, e.g. the overwhelming majority of web content, then a visitor's session id, by definition, cannot be linked to their personal information, because there is no personal information to link to.

However, if a session id is used to track "the same user across different websites", building up a behavioural profile, THAT would require explicit consent. But since cookies are per-domain, and browsers have severely locked down cross domain access, that's basically a non-existence concern (as both a blessing and a curse. The wild west web is long gone, for better and for worse).