System Preferences - 'Allow the apps below to control your computer'. What is the extent of 'control'?
As you saw in your research, the accessibility api allows one app to control other apps on your computer, in much the same way you do with your mouse and keyboard. These apps can resize windows, click buttons, type words, copy and paste, etc.
If you want an app to be able to do any of these things for you, you will need to grant access to the accessibility api (ie, &quot;allow it to control your computer&quot;). If you'd rather it not have that ability, or if there's no reason for it to have that ability, deny access.
Zoom is an example of an app that I do not allow to use the accessibility API. It asks, but I don't know why, because there's no reason Zoom should ever need to click or type in my place.