Gabrielle,
Happy to hear back from you.
Thanks for taking a look over those steps. If you're not finding the specific website in the Search field, then it may be cleared already.
Let's see if this happens with a different browser. Since you mentioned this only seems to be happening with the links shared under the Support tab in About This Mac, we'll need to change the default browser temporarily to test this out.
To do this, close the About This Mac window if it's still open. Then, navigate to System Preferences > General > Default web browser, and set this to another browser you have installed other than Safari. If you don't have another browser installed, go to the Mac App Store and download one for free, like Google Chrome for example.
Once you have the default browser changed, open About This Mac once again and navigate to the Support tab to open one or more of the listed links there (test more than one please). Let us know if the same redirect continues. This will help us identify if there is a break in the links from that section in About This Mac, or if it's an issue with Safari itself saving the old website data.
Thanks!