Hi Adam, you likely need to enable the new field on your feature layer view. If you open the view in the map viewer, you should see an option in the layer menu "Set View Definition" -> "Define Fields":
In the "Define Fields" dialog, you should then see the fields you've added:
If you still don't see the new fields, probably best to contact Technical Support to figure out what is happening. Ultimately as Khaled mentioned, feature layer views do inherit fields added to the primary layer. They are just disabled from the view until explicitly enabled by you. This is to maintain data security - say you add a field with sensitive info to your private primary layer that has public views. If the field were to automatically show, the data would be exposed before you had the opportunity to disable.
note - and as Russ mentioned, if the layer was created using Survey123, field inheritance may be disabled.
Cheers,
Chris