The ground doesn’t carry the different voltages, but it does carry the return currents. This can cause slight voltage differences in ground at various points, but is generally not a problem for well designed components.

The RC servo signal is a fairly high voltage pulse where the duration/width is important and is typically reasonably immune to slight ground voltage variation/noise.

It’s considered poor practice to have any ground loops, they can cause issues. The grounds should either be connected daisy chain style, the normal RC way, battery to esc to receiver to servo, but not servo back to battery which creates a ground loop. Or the star method, from battery to each component without any interconnecting grounds.

If the typical daisy chain style doesn’t provide the servo enough power, perhaps try running a ground to it directly from the BEC, but remove the receiver to servo ground.