It's not that complicated. It's all about the physical scale of the image you see. If the scale changes, then sensitivity changes as well and you need to adjust the cm/360 to fix it. Treat the monitor as a window that you look through.
Think of the resolution, fov, and monitor as an image resizer. If any of these change the physical size of the image, then you need to change your cm/360 by the same amount (monitor distance 0%).
You will need to change the cm/360 in these cases because they will change physical size of the game:
Different fov on the same monitor
Same fov on different sized monitors
Reducing resolution without upscaling
Changing aspect ratio in a horizontal fov game
Start with 103 fov at 1080p
If you reduce the resolution to 720p without upscaling it, then you have shrank the physical size of the image by 66.67% of the original size.
You will want to reduce your cm/360 to 66.66% of the original value as well.
This is identical to zooming out 1.5x to ~124 fov. (2 * atan(3/2 * tan(103/2 * pi/180)) * 180/pi = ~124).
This shows that the resolution can be used as an FOV slider if you want, you just don't get to see the extra fov since its black.
Here we change the fov to 162 fov. It is a 5x zoom difference. It practically shrank the image to 20% of the original, so your cm/360 needs to shrink to 20% of the original value as well.
Here is 103 fov resized to 20%, overlayed on the 162 fov. If this monitor was 5x larger than the above, then there would be no need to change the cm/360. The physical size of the 103 fov area in yellow would be identical to the monitor above. Since the monitor is basically a window that you are looking through, the 5x bigger window provides the extra fov.
Here is the 162 fov image resized 500%. You can see that it's identical to 103 fov.
If you reduce the resolution width to go from 16:9 to 4:3, and it only crops off the sides, then there is no change to the physical size of the image and no change to the sensitivity.
If the game uses horizontal fov though, and it tries to keep the 103 on 1440px instead of 1920px, then there is a 75% scale difference (1440/1920). So your cm/360 needs to be 75% of the original value as well.
This 75% reduction results in an equivalent fov of ~118 (2 * atan(1920/1440 * tan(103/2 * pi/180)) * 180/pi).