I did some more testing.
Set up #1:
Using the custom basemap in the local county coordinate system, then publishing the hosted feature service in that same local county coordinate system. The GNSS input is always NAD 1983 (2011).
Transformation is NAD_1983_HARN_To_NAD_1983_2011 in Esri Field Maps.
Set up #2:
Data, custom basemap, and GNSS output is all in NAD 1983 (2011).
No transformation is occurring in field maps, but then post-processing of the data occurs by projecting the data to the local county coordinate system in ArcGIS Pro.
I tested on two devices with varying accuracy levels. One was an Eos Arrow Gold CM Receiver. I actually ended up having more accurate results with the Set Up #1 with the hosted feature service being in the local county coordinate system than it being in NAD 1983 (2011) for Z values. X and Y were pretty comparable. With this data in the local county coordinate system already, it seems to make more sense to stick with set up #1. Is my thought process off on this?