https://myactivity.google.com/u/1/activitycontrols
Disabling a setting asks if you also want to delete your history for that setting; if you say yes it shows a sample of what you're deleting, you confirm it, and it's done. Nothing tried to encourage me to stick around, keep my data, they could easily have let me turn off collection of new data but not mentioned that they still have the existing data around -- I expected trickery but found none.
(Except for one small detail: I can't figure out how one is supposed to discover that this page exists in the first place; the support update we're discussing contains a link to it, but I can't find it anywhere in the YouTube preferences or advanced settings or anywhere else.)
(Oh, and it had no visible effect on my YouTube home screen, I'm not seeing the empty page I hoped for, just the same garbage videos it usually prompts me with for no clear reason. So there's that too.)