How to remove DC offset (and make average DC value 0V) from ADS1261 square wave AC-excitation circuit
You tried 2 values 4 orders of magnitude apart.

In the first (15nF) example, the capacitance is too small.  Your DC content is being removed, but with a time constant of 150us, the capacitor is almost completely charged before you get to the next edge of the 1KHz square wave.  As such, the output is near zero at each edge, and shows the entire 5V P-P transition.

In the second (100uF) example, you have a time constant of about 1s.  The cap in the simulation is initialized to 2.5V, and in the 2ms time frame of your scan, it doesn't change much.  Therefore, the output remains 2.5V above the input.  If you run that simulation for a few seconds, you'll see the waveform you want.

Your challenge is to determine a value that doesn't distort too much, but settles quickly enough for your purposes.