Do you still have the map you created above available in AGOL? If so, go to the overview and hit "Open in Field Maps Designer". Let it open the designer. Close the designer, and open the map in Field Maps and see if the fields are in the same order which you set them in in the Pop-Up configuration. The order of the fields in the Pop-Up must be different than from the order of the fields in the original attribute table to test this.
I thought any time I click on the Field Maps Designer, regardless of making changes in the designer, it had been re-ordering the fields to what I described previously, it maintains the fields checked in the Pop-Up Configuration, but they are in order based on the fields in the original attribute table. Now I am not sure after additional testing, as I can't get any of the previous templates to work correctly so I can recreate what I thought was happening, at this time.
"In my testing, if I delete all the Form entries, then "Convert Popup" in the Forms panel, it will add all the values from the configured popup and maintain the order." I get the same behavior, if I convert the pop-up to the form for the incorrect maps, it works as intended.
I don't use the Field Maps Designer because we have multiple sites spread throughout the country so I have a template set up in ArcPro that was working as intended up until recently. Modifying 80+ Layers in Field Maps Designer is time consuming when you have 30 different sites/maps to do this for.
I went back to an earlier version of my Template and tested sharing it. It's altering the fields even weirder. Some of the layers fields are in order of the Pop-Up configuration and some of them are in order of the attribute table field order while some moved one field to the top of the list, but the rest of the fields are in order of the Pop-Up.
I may try testing on our Portal to see if the behavior is the same there.
Thanks for your assistance thus far!