You’ve probably noticed when you enter other online checkout flows it feels like you're in a different version of the site. It is usually much more stripped back. The header loses a lot of its links, the site-wide navigation disappears, and the footer links go, to be replaced with just basic copyright and legal notes.
The links should be reduced because you don't want users getting distracted when they're in the checkout flow. This is a key point of the journey where they've expressed a strong interest in buying, so make it as easy as possible for them to do that. If they suddenly spot a new product on the navigation they may click it, read about this new product, compare it to one on another site, and forget to convert with you.
People ask if there should be *any* links at all, and some checkout flows have a few but I tend to design them with none (other than ones to other checkout steps). This includes removing the link to the homepage from the logo. It just makes things clearer and more focussed. If the user wants to leave there's always a browser back button or they can close the window altogether.