[Python] How to achieve consistent scaling of spectrograms with new and old scipy APIs

In making spectrograms with scipy.signal.spectrogram and scipy.signal.ShortTimeFFT I expect to get numerically similar outputs, but instead the magnitudes of the outputs are very different. I don't understand what parameters will lead to equivalent results.

Following the examples in the docs, I make a magnitude spectrogram in three ways. Instead of having similar magnitudes, they have completely different magnitudes

import scipy
import numpy as np
np.random.seed(0)
x=np.random.random(1000)

noverlap=50
fs=1000
nperseg=100
N=len(x)

f1,t1, s1 = scipy.signal.spectrogram(x,fs=fs, scaling='spectrum', nperseg=nperseg, noverlap=noverlap, mode='magnitude')

stfft = scipy.signal.ShortTimeFFT.from_window(('tukey', 0.25), fs=1000, nperseg=100, noverlap=50, fft_mode='onesided',
scale_to='magnitude', phase_shift=None)
s2 = stfft.spectrogram(x)

SFT = scipy.signal.ShortTimeFFT.from_window(('tukey',.25), fs=fs, nperseg=nperseg, noverlap=noverlap,
fft_mode='onesided',
scale_to='magnitude', phase_shift=None)
Sz3 = SFT.stft(x, p0=0, p1=(N-noverlap)//SFT.hop, k_offset=nperseg//2)
t3 = SFT.t(N, p0=0, p1=(N-noverlap)//SFT.hop, k_offset=nperseg//2)
s3 = np.sqrt(Sz3.real**2 + Sz3.imag**2)

s1.mean(), s2.mean(), s3.mean()
# output: (0.026607584897909715, 0.0056786357567832615, 0.038652586739534416)


I realize that the exact values for s2 will be different because of different handling of time-bins at the edges, but the mean magnitude should be roughly similar, and I think s1 and s2 should have the same values.

Why are these different? What parameters will lead to similar results for scipy.signal.spectrogram and scipy.signal.ShrotTimeFFT, when using one-sided and magnitude (as opposed to psd) scaling?

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