Assuming they do it correctly, you get added to that brands unsubscribe list. They then need to share that list with all their email partners. The email partners download yoaded lists once per week, so it can take that long to stop receiving emails.
If it's a site that does all their own email you shouldn't get any emails after unsubscribing.
In the U.S., the CAN-SPAM act requires companies to honor your opt out/unsubscribe request within 10 days. For particularly agressive mailing lists that don't honor unsubscribes I will happily report them as spam to my email provider, report them to the FTC, and send a cease and desist letter I generated with chatGPT to their legal@example.com mailbox.
In the EU, GDPR has made spam levels drop, and when the occasional one gets through the unsubscribe link works instantly because they don't want you to get to the point of asking "wait where did you get my address".
I've just stopped unsubscribing from email lists these days and instead I mark them as spam on Gmail so that Gmail can identify what they are for everyone else. Saw an article a while back with political fundraiser people begging people to stop marking them as spam and its just like, that's what happens when you keep subscribing me to new lists I never signed up for after I unsubscribe from the ones I'm on. If I go out of my way to inform you that email spam won't convince me to donate (which I do plenty of on my own without prompting) then you should listen to me.
Building and setting up emails, email lists, and opt lists/forms shouldn’t take days. It should be automated and done the very second a recipient opts out. If they don’t then you should be trusting them with your business.