This is what happens, when the Auto button is activated, it means Lr has loaded the full resolution negative. So the Auto is computed based on this full resolution negative.
When you apply Auto to a batch of photos, for performance reasons, Lightroom loads a lower resolution negatives cached in the camera raw cache (like Smart Previews) and computes Auto from that. Since the two input are different, the results could differ slightly.
BTW, the issue exists in the previous version of Lightroom as well. It is just that the new Auto shows more differences. To summarize, it is a performance vs accuracy tradeoff.
The table below shows the results of applying Auto Tone to seven pseudo-randomly chosen unprocessed raw photos from different cameras. All the results had a standard preview size of 1440.
Row 1: After doing Reset and Auto Tone in Develop.
Row 2: After doing Preferences > Camera Raw Cache Settings > Purge Cache; exit LR; delete Previews.lrdata; restart LR; Build 1:1 Previews; select 7 photos; Quick Develop > Auto.
Row 3: After steps in row 2, then Discard 1:1 Previews; Purge Cache; Build 1:1 Previews; Quick Develop > Auto.
Row 4: After Purge Cache; exit LR; delete Previews.lrdata; restart LR; Build Standard Previews.
Based on what Simon described, this makes me suspicious that the Purge Cache command may not be fully flushing the raw cache.
I apply a preset to batches in Library's Quick Develop that includes Auto (Latest LR Classic). But I don't see any difference between applying it to a batch of files that way, and applying it individually in Develop. Thinking about this, I suspect this is because I don't use the ACR cache in LR. Yes, I have one set, but I have also set it to Read Only and it is empty (deliberately). I have a pretty fast computer and don't think using the ACR cache produces any noticeable speed-up for me, so I prefer to remove that unnecessary task from LR (it already has far too much to do IMO).
So I presume that applying my preset with Auto in Library (with Quick Develop) makes LR render a full preview for each file as it does not have a half-baked one in the ACR cache. Am I right in my thinking or have I missed something?