If cosmic expansion magically stopped today, how would the night sky change?

It would gradually brighten over billions of years as formerly redshifted light shifted back into the visible range

The current darkness relies heavily on the ongoing recession velocity of distant galaxies causing redshift. If the expansion of space were instantaneously halted, the spectral stretching effect would cease to dominate the light budget moving forward. Light emitted from extremely distant sources that was previously redshifted far into the infrared or microwave regions would no longer undergo further redshift. Over the next few billion years, the light already in transit that had been pushed out of the visible spectrum would effectively 'catch up' spectrally, shifting back toward visible wavelengths. This gradual reversal of redshift would cause the night sky to brighten incrementally until the visibility was limited solely by the age horizon.