UPDATE 3/14/2023
This is now possible in the Field Maps configuration app. https://doc.arcgis.com/en/field-maps/android/help/configure-the-map.htm#ESRI_SECTION1_93E449067ECE492D825A1C71A31EF8EF
However, as far as I know, there is still not a way to update feature templates in the "new" map viewer. You must use ArcGIS Pro or MapViewer Classic.
ORIGINAL POST
Adding a template to an existing map in Field Maps can be confusing as there are multiple ways to make it look like it should work, but not all actually update into Field Maps.
First how to do it correctly (as of 7/19/2022):
Carefully follow the directions provided in the documentation.
Note, that this only works in Map Viewer Classic and there you have to start editing features, then click Manage at the bottom of the templates list, and create a new template. If a field has a domain, be sure to enter a valid domain value into the text box as there is no validation.
How NOT to do, but make it look like it should work:
In ANY map editor, add a domain to a field, then use unique symbol renderer to define a symbol based on that domain. Interestingly, doing this will show features in the template list from the method above but the results will not make it into field maps.
Hopefully this is cleaned up soon so that it works with the new map viewer and either templates are tied to symbology or there is some notification that changes to symbology do not affect edit templates.