Hello Thunderclutch,
Welcome to the Apple Support Communities. We know how concerning it can be when a feature you're accustomed to using is not appearing as it has in the past. We understand that you're currently not seeing the Reader View icon in the Smart Search Field with Safari 14.0.2.
We checked the link from New York Review of Books that you provided on a couple of different machines running different versions of Safari (14.0.1, 14.0.2. We were able to see the Reader button as expected and described in this article: Hide ads when reading articles in Safari on Mac.
Since this isn't occurring on your device, please follow these troubleshooting steps to begin:
1 - Quit all apps. If an app will not quit, follow these steps to force it to quit: How to force an app to quit on your Mac.
2 - Restart your Mac: Go to the Apple menu in the top left corner of your screen > Restart.
3 - Hold down the shift key on the left side of the keyboard as you click on the Safari app to launch it. This allows the app to bypass the last saved state for the app. When the app begins bouncing in the dock, you can release the shift key. Once the app is up and running, see if there is any change with Safari when you navigate to the New York Review of Books site for instance. It may take a couple of moments for the button to appear.
4 - If you're still not seeing the Reader button, restart in safe mode and test again: How to use safe mode on your Mac.
5 - If still not appearing in safe mode you’ll need to create a new user, sign into that new user with your information, and test it out again. This article will show you how: Set up users, guests, and groups on Mac.
Let us know the results.
All the best.