No, that button is enough. That button did not exist on older versions, so you definitely did not click it if it did not work. If you're running the version of macOS that was released over a year ago (Monterey) or running Ventura (released more recently), then the button will exist.

https://support.apple.com/en-us/HT208987

"Other ways to disable Activation Lock"

"Activation Lock is disabled when you use the Erase All Content and Settings feature."

Apple confirms that the feature works exactly as I said and exactly as users expect. I've used it myself, and it does work.

Users running software that is several major versions out of date will have a more difficult experience, since that button did not exist, and they would have to first remove Activation Lock before going into Recovery Mode to manually format the Mac. Those are the remaining steps that were linked several comments up from here: https://news.ycombinator.com/item?id=34505523

Apple has made the process as easy as it possible can be now, identical to the process used to factory reset an iPhone.