Hey there, cmwales!
Thanks for linking to the article. It's interesting that the functionality is not available to you. I checked with a few other Community Managers but none of us are currently using the S8 or a Samsung device that's running Oreo. I was hoping other Samsung users would jump on here. Let me check with our Samsung team to see what info I can hunt down for you. In the meantime, can you confirm that you're using the S8 and also provide me with baseband version of your device?
You can go into home screen settings and turn the badges off. This is inline with Google Oreo changes.
Hold down on an empty space on the home screen then tap on settings. You will find the badge toggle.
A little late on this, however I have a an S9 and last week I had the option to clear badges and now I do not. After reading your post, I realize that it was after an update. As far as the advice offered to your original question, it doesn't relate. Disabling notification numbers on the badges is not the same as being able to clear them individually on demand.