I invariably see Safari Networking climb to 100+% when I visit nytimes.com, even with extensions disabled (which I just tried once more to be certain).
It appears to be at 0% under ordinary circumstances, just rising and falling back to 0% as I click on links.
Networking should rise when you click on any link, and with a content rich site like NYT it should rise a lot. Every page has multiple links to other pages which must be opened, and often those have links to still more content that have to be opened. It is a virtual cascade of links to be resolved. Be that as it may, driving your system to 100% of a core and causing the fan to spin up to seems excessive. I don't like to use Activity Monitor in that way because it is often among the top three or four CPU users on my system and because of that it distorts the results preferring instead Marcel Bresink's System Monitor
which shows the individual cores, but it only identifies the top 5 apps. I am using Safari 14.0.3 and as far as I can tell it generally uses one of the low performance cores and seldom, if ever, switches to a high speed core.
I guess it's safe to post at this point...
I'll spare you the gory details except to say that part of my problem was that I've heard "If the problem doesn't follow you to a test account it's in your home folder" so many times that it never occurred to me that it might actually be an app that didn't follow me, and, indeed, it turned out to be Cookie.
I had Cookie's timer set to delete non-favorite cookies, tracking cookies, and cache every 60 seconds, and that configuration worked just fine through Catalina, but something changed in Big Sur, and deleting cache somehow began causing Safari Networking to spike irredeemably.
I unchecked the box, and the process has spiked only once in the past two days, as opposed to multiple times every hour.
Appendix 1: I agree that a third party app could be more useful than Activity Monitor in many instances, but it was quite sufficient in this one
Appendix 2: I discovered a bug in Safari 14 that affects troubleshooting: Hitting either Safari > Develop > Disable Extensions or command-E immediately results in your tool bar icons disappearing and Safari > Prefs > Extensions showing no extensions, BUT it doesn't disable your extensions until you quit/relaunch Safari, as opposed to their being disabled immediately as they have been.