If Doppler effect in light is taught, only the moving-source scenario is discussed, for the simple reason that in the moving-observer scenario the speed of light is explicitly variable. If the moving-observer scenario is taught, either light is not mentioned at all, in 99% of the cases, or enough confusion is introduced so that the variability of the speed of light relative to the moving observer is camouflaged:

Doppler Effect: Moving Observer https://www.youtube.com/watch?v=UHpPsnJNKrk

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