I suspect in your case what has gone wrong is the detection of what was white in the image: I think the big chunk of blue sky in the top-left has fooled something into thinking that this was white, and deciding that the colour temperature was that of the sky (which is not a very good black body in the first place, but in so far as it is has a very high ...
Because you did not also increase the chroma contrast. As a 1st order approximation the perceived saturation goes with the chroma : luma ratio, best kept constant.
No, that would be due the Hunt effect, and it is a matter of human color appearance versus simplified math.
While there are multiple ways to do this, my preferred approach is exposure blending. You basically take multiple exposures from LR and blend them together in Photoshop using luminosity masks. You may not even need 3 exposures to get a satisfactory product if you start with the right settings in LR to generate the first image. I took the 3rd exposure you ...
Take a look at DarkTable ... Equalizer ... Luma
Drag up the center to center-right for increase contrast in higher frequencies.
This may be a starting point to make the stars "pop", but it doesn't address color shifts or other adjustments you may want to make.