I brought this to Esri Support's attention already (and they suggested I bring it up here), but have a permanent fix in place for the issue brought up in https://community.esri.com/t5/arcgis-field-maps-questions/labels-not-showing-up-in-field-maps/m-p/11....
Basically, I made a change to a layer in the "Visualization" tab, saved it, and then whatever I had for labels in my web map was no longer showing on for mobile device web maps (though it was showing on desktop).
What was happening here was that me saving in "Visualization" was overwriting whatever I had for labels in the web map. So, the solution was me going back into "Visualization", turn on labels from here, re-save, and then labels appeared as they should for web maps viewed in my mobile devices.
So, my idea is to fix this?