this is going to sound a bit weird maybe, but try to visualize.
I have a certain bounding box of 200x200 units. I want to calculate at what distance to the camera this object is potentionally 10% or more of the screen it’s resolution. I want to precalculate this, so i can make a trigger sphere to avoid over calculating.
Is your bounding box 2D or 3D? I’m assuming 3D here, it’s even easier in 2D ;).
You could use Camera.WorldToScreenPoint to transform each of the 8 corner points of your bounding volume to screen space. To get a quick overestimate of the screen size, you could add these transformed points in a Bounds struct with Bounds.Encapsulate(). The resulting width and height of the bounds can have significant overestimation depending on the orientation and shape of your original bounding volume.
Considering, you’re pre-calculating, it should be good enough.
However, if you need more precision, you could calculate the screen space size of each of the front facing sides of your bounds and add those together. But since that’s only precise for one given viewing angle, I doubt this will be worth it for your case.