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The "crop factor" is a bit of a misnomer as it doesn't really do anything other than describe field of view differences.
Take a telescope for instance. I have a 130mm F/5.2 refractor which I have used with multiple cameras; ASI1600/QHY163M, Nikon D7200 and Nikon D810/ASI094. The first is a M4/3, the second APS-C and finally the last is FF.
Using the crop factor logic I have a 2x (1350mm), 1.6x (1080mm) and 1x (675mm). In all of this the aperture, focal length and focal ratio have not changed and it doesn't matter what camera you have, it has no affect on the focal ratio because neither the physical focal length or aperture have changed.
Now you are correct in that TECHNICALLY using the crop factor would make it a 130mm F/10.4 IF you were to use absolute comparisons between a M4/3 and a FF. This is only applicable if you're saying one lens is like another (your first comparison).
You're camera isn't misleading you though because you're not talking back technicalities about actually taking photos. Using an APS-C doesn't magically change a 50mm F/4 to a 80mm F/6, only that you would get the same amount of light output and FOV as a 50mm F/4.
In real life you are still shooting with a 50mm F/4 because your lens has a 12.5mm aperture and a 50mm focal length regardless of whether you're using a M4/3. an APS-C or FF.
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