Let’s start dealing with some chord shifting by altering in between G and C chords on each beat (Example 6). See TAB+N otation here: https://acousticguitar.com/practice-with-a-metronome-to-shift-between-chords/.
Enable your fingers to change as slowly as needed for a smooth transition. If the open strings continue to sound out as you swap chord fingerings, don’t fret about it for now– it’s far more essential to concentrate on getting your fingers into the right location at the correct time. With practice, the amount of time it considers you to make those switches will start to decrease.