What happens when you refuse to accept cookies?

Your waiter gets sad because their tip will be smaller :)

... oh! You mean browser cookies?

If you inspect the sessions, you'll find - in general - less traffic going from your computer to external sources (especially with third-party trackers and the like)

you'll also probably get notably less personalization and/or "remembering where you left off when you come back" type interaction on a given site

It depends. Is it a French website? You can click on something that says "Continuer sans accepter" (Continue/proceed without accepting) and continue your visit.

Some websites have check-boxes on what you accept, and a button that says "Tout refuser" (refuse all). You can click that and proceed with your visit.

You can accept cookies but disable third party cookies. Third party cookies are the root of all evil and also the foundation of Google's business model.

I can’t say for sure, but what I can say is that there are plenty of methods to track a user which doesn’t leave a breadcrumb on the users device.

Most websites I visited then denied my visit; finally I settled by using an ad blocker to block their prompts.