Yes everything is expanding like that.
Look back to the red shifted light.
When a white star starts with white light, has the literal wavelength expanded to be more red looking.
https://www.esa.int/Science_Exploration/Space_Science/What_is_red_shift
It’s the literal light getting shifted. So the speed of light is the same, but the distance it travels in a given time is not. Making it red shifted.
So you assume the speed of light is the same between references frames. There not. It’s always the same. The definition of a second changes such that the speed of light is always the same.
That’s relativity.