The default parameters from Klipper, as well as the Elegoo distributed settings, allow for a lot of error and inaccuracy from the z probe. We can improve on this in terms of performance and accuracy.

Tune your z probe stanza in printer.cfg to improve probe accuracy by decreasing samples_tolerance. Its Klipper default is 0.100mm meaning you’re accepting probe results that are off by hundreds of microns while the probe is precise with readings below 0.00250mm, so using a value of closer to 0.00333 - 0.00750 is much more reasonable and accurate.

Given a tighter tolerance we can also speed things up by only two (2) probe readings that now will need to more closely agree. So we'll also increase samples_tolerance_retries as well, We just need close agreement in the readings so we didn’t catch the plate as it was thermally changing. Switch from Median to Average as a median for two points isn't sensible and the average will split the simple difference between the two readings if they don't agree exactly.

This should leave you with a [Probe] stanza in printer,cfg that looks something like this:

[probe]
pin:^PA11
x_offset: -24.25
y_offset: 20.45
z_offset: 0.0 		# more on this and probe calibration later
speed: 10.0
samples: 2
samples_result: average
sample_retract_dist: 3.0
samples_tolerance:	0.00500
samples_tolerance_retries: 7