Hi Eulalie,
> I am looking for documentation or examples to publish a new Survey123 with a REST API.
I don't believe it is possible to create a new survey for Survey123 for ArcGIS with the REST API.
FYI, a module for Survey123 was just added to the ArcGIS API for Python,
The Next BIG Thing: The API for Python 1.5.1 Appears
But it currently, only allows users and administrators of Survey 123 Surveys to analysis, report on , and access the data for various surveys.
Hope this helps,