> I can't figure out how one is supposed to discover that this page exists in the first place
Click on "History" in the YouTube sidebar. It'll take you to https://www.youtube.com/feed/history. Not only does it shows the watch history, it has embedded controls for clearing the entire history, deleting individual entries, turning off new collection, as well as links to the more granular activity control pages.
You're absolutely right, thank you. I was so hung up on "preferences" or "settings" being the place to look that I missed the link that was literally named the thing I was looking for!
Click on "History" in the YouTube sidebar. It'll take you to https://www.youtube.com/feed/history. Not only does it shows the watch history, it has embedded controls for clearing the entire history, deleting individual entries, turning off new collection, as well as links to the more granular activity control pages.