I’m more a photographer than an astronomer but as far as I understand it those false coloured images are produced by monochrome sensors that are sensitive to a broad range of frequencies which have filters placed in front of the sensor to seperate out a specific frequency and then to create a single image they will photograph with different filters to get various “colours” then that data is mapped to the colour your monitor can display.
Whether the colour is true to life is a really complicated question for basically any photo you see lol. like, there is no simple objective answer for any photo imho unless it’s obviously a no