Help me understand this aspect of aperture, please

Sensor size doesn't actually affect anything for that really. A lens will project an image circle onto the focal plane of the camera, and the sensor (or film) then sits there. A crop sensor merely uses a smaller portion of it, but the same amount of light per square mm falls on it regardless of whether that sensor is an APS-C, 35mm full frame, medium format, or what have you. Any of the extra focused light is just 'wasted'.

If you add additional optics to the system to refocus all that extra light into the smaller sensor, then you have effectively changed the focal length, and therefore are changing your ratio as well.

*Edit:*
Larger sensors often 'do better' with lower light because their sensor sites for each pixel can be larger while maintaining a reasonable total pixel count. Crop bodies have to pack them in tighter simply because they're physically smaller. The larger sensor sites of the full frame cameras offer a more reliable read on their data for a number of reasons, which makes higher ISO settings appear far cleaner.

camera sensor/ film format has NOTHING to do with F number as said above.
But it is important to remember that the image formed in the focal plane, always has a brighter center zone and the more you move toward the corners of the image's circle periphery, there is more "Light Fall Off". That is why if you use a non dedicated lens on a large format camera, you will have more darker corners of image. That BTW is also called "Vignette" effect. Though this phenomenon is less prominent when a cropped APC lens is used for FF 35mm sensor / film camera, it is always there and becomes really noticeable if use that same 35mm lens on a medium, or better, a true large format film box camera.

So Format of camera doesn't do anything with F number but, you don't have a homogeneous light formed image at the plane of focus, from center to periphery ALL the time. You will see that vignette effect better in a large format.