I've implemented MapServer's 8.0.0 TinyOWS for (WFST), CrunchyData's pg_featureserv 1.2.0 (OGC API), and GeoServer's 2.21.2 (WFS) services for a point layer I have in PostGIS. I can get capabilities, metadata, individual features, and attribute tables from all three.
However, they all only work with "Snapshot" in the feature Properties in ArcGIS Pro 2.9 (the full dataset or a random-thin of the full dataset). When I change it to "On Demand" so that I can only retrieve what is in view extents, there is simply nothing displayed and no attributes. I've manually made calls to these server implementations with postman and I know that I can either bbox or feature number limit on all three. (I also know that ArcGIS Pro's Feature Limit works on the properties tab below "Snapshot/On Demand").
Posts from 2017 state that Pro will support extent based querying, and the docs say that "On Demand works but compatibility is less widespread."
At this point all I can guess is to try to intercept the calls that Esri is making to make sure that they're valid calls or malformed, or find the right server technology to make sure that I can deliver subsets of data on a feature level.