What the OP is seeing in lower and lower noise as the averaging duration increases makes sense as the capture duration itself has not changed. It is the duration of the capture that will limit the effects of the lower frequency noise contributions. The averaging is a low pass filter (a frequency response in the shape of a Sinc), so given a single capture with total noise $P$, increasing the span of the moving average will effectively lower the bandwidth of the filter and therefore reduce how much of $P$ gets through the filter. Since the noise density is increasing as we approach DC, the benefit of the filtering will get progressively less, which is exactly what we are seeing.
What the ADEV curve is informing us is the total duration of the capture to minimize the total noise power $P$: with white noise, $P$ is constant regardless of capture duration, but with pink noise, with the spectrum increasing at 10 dB/decade as we approach DC, longer observations lead to an increase in total noise power. This is because the total duration of the capture sets the low frequency cutoff for the total noise in the signal: for a capture length of $T$ seconds, the process of the finite duration capture is effectively a high pass filter with a cutoff freq of $1/T$ (consider that it takes an infinite amount of time to truly observe DC).
I made a demonstration to help clarify this with an example noise signal that has a $1/f^2$, $1/f$ and white noise component as shown in the spectrum below. Here we see what I mentioned above with regards to noise increasing as we approach DC: and here with white noise clearly above 100KHz, if we only observed this for 10 us, we would not measure the elevated noise effects from the $1/f$ portions at 10 KHz and lower:
The ADEV for this example noise was computed as follows, and the conclusion from this is we can operate on captures up to about 200 samples while assuming stationarity in the signal. Specifically for the durations where the ADEV curve is going down at $1/\sqrt{\tau}$ it means we have a white noise condition, a stationary signal with power independent of capture length:
The result for the moving average on this example noise data at different averaging times matches the OP's result and the intuition provided above, that with the moving average we are simply filtering the same noise process with a tighter and tighter low pass filter: the total noise as given by the standard deviation of the output after the moving average will always go down as averaging time is increased, but in the process we only have a narrower usable spectrum to work with.
However below is a plot where I show the computed standard deviations vs block length within the same data. For shorter durations up through the time the ADEV plot is going down at $1/\sqrt{\tau}$ we expect the standard deviation to remain constant. It appears to go down at 10 seconds, but the data is 1 sample/sec so there are insignificant samples to get an accurate standard deviation at this time duration. What we do see is the gradual increase in standard deviation as we go past 100 seconds and beyond consistent with the floor in the ADEV, and then increasing significantly as we continue beyond that.
Consider the time series of the captured data directly as plotted below. Here we see the characteristics of a non-stationary signal where the longer we observe the further away we get from the starting position. We can take the average of the entire sequence to get the mean, but if we continue to observe longer, there will be a completely different mean. The averaging we choose to do is set by the bandwidth of the actual signal we are interested in, such that we minimize noise that is outside of this bandwidth. Also we see how the total noise (as given by the total deviations) will increase the longer we make the capture. A longer capture is necessary if we also want to observe low frequency signals, otherwise a high pass filter can be used to eliminate the noise elevation (and make the signal stationary)- this is what the ADEV computation does to provide consistent metrics for non-stationary signals. We see here that over much shorter capture durations the shorter capture itself has all the characteristics of a stationary process (within that capture the mean and standard deviation are relatively constant). With review of the ADEV we see that this assumption holds up pretty well out to 100 seconds. The plot below extends out to 4 million seconds.
Control Test with White Noise
Below is the experiment above repeated with a white noise test signal, First showing the ADEV:
And then the standard deviation vs block averaging interval:
For completeness of intuition, I include a time series capture below for the white noise data used above, where we see the characteristics of a stationary process (mean and standard deviation do not change with capture duration).
Conclusions with Regards to ADC Capture
The sampling rate sets the usable bandwidth according to Nyquist. The total noise power within that bandwidth will increase with capture duration if we have 1/f noise present or will remain constant if the noise is indeed white stationary noise over the duration of capture. If we subsequently perform low pass filtering (moving average) we are reducing the usable bandwidth (and can subsequently reduce the sampling rate - such as done with decimation), with a corresponding reduction in total noise. This is exactly what the OP is seeing, and the longer the average, the tighter that filter (on the same original process of a fixed total duration) and therefore the resulting total noise will keep going down.
The floor in the ADEV curve informs us of how long the signal can reasonably be assumed to be stationary, and with that, the total noise power for any capture duration up to that time will remain constant. Beyond that duration with longer captures we will start to see an increase in total noise power. The OP is averaging for longer and longer intervals, which is reducing the total noise but also reducing the bandwidth available for any signals of interest.
The upturn in ADEV is an indication that the signal as captured is no longer stationary. Not stationary meaning that if we were to continue to increase the duration, any estimate of the mean will be varying and standard deviation will be increasing as the capture length increases. This is in contrast to a captured signal that was stationary, where the error itself in our estimate of the mean and standard deviation would get progressively smaller as the capture duration increases (and converge to the "true" mean and standard deviation). Therefore the ADEV tells us the degree of stability over a given time duration for the variable of interest.
