You're 80% there.
If you use the same lens on a crop sensor, and back up for the same composition, which gives more DoF and why? They both have the same FoV.
In post 20 I stated that the focus tolerance (depth of focus) at the sensor is controlled
only by the aperture diameter (in mm) and subject distance.
If you use a shorter focal length lens at the same f#; that is actually a smaller aperture diameter, which increases the focus tolerance. Or, if you move back to keep the composition the same, using the same lens and f#; the subject distance increases, which increases the focus tolerance.
The focus tolerance dictates how sharp things are relative to each other, as recorded by the sensor. And it is the focus tolerance that most are actually talking about when they talk about depth of field.
However, depth of field is actually a variable; and it is dependent on the magnification at which the focus tolerance is viewed...
Depth of field is your
perception of acceptable sharpness. That is why a depth of field calculator uses a circle of confusion limit which is predicated on a display size and viewing distance (standard viewing conditions by a person w/ average eyesight).
Anything that increases the magnification of the focus tolerance reduces the perceived depth of field... that can be lens magnification, it can be cropping and enlarging (sensor/post), or more critical viewing from a shorter distance. All of those things are really just different versions of cropping/magnifying the scene/light.
Take an image of marginal sharpness and display it on your monitor so that the flaws are apparent. Now make it smaller so that the flaws are not apparent... it looks sharper. Now make it larger again to where it looks bad, then get up and move a distance away to where the flaws are not apparent again... it looks sharper again. THAT is depth of field in practice... while the recorded focus tolerance/depth of focus has remained constant.
How aperture diameter affects focus tolerance/depth of focus (the narrow aperture rays are also inside of the wide aperture; just not depicted for simplicity/clarity)
View attachment 312263