Hello Arthur Kopelman,
Are you using ArcGIS Online or ArcGIS Enterprise? Depending on your Web GIS infrastructure the answer may vary.
If you are using ArcGIS Enterprise are you creating and publishing surveys based on existing feature services?
Are you publishing a hosted feature service with your survey?
If you are using a registered service the export capabilities are going to be managed from ArcGIS Server manager on the service level.
If you are using a hosted feature service on the Item Details page under the settings at the very bottom there should be an option to enable or disable "Export Data".
If you are unsure if the service is hosted or not the easiest way to tell is on the Item Details page Overview right next to the thumbnail it will say "Feature Layer (hosted)" if it is hosted if it does not have that (hosted) next to it the service may have been added to ArcGIS Online as an item or in Enterprise it is a registered service.
If the service is indeed a hosted feature service and the ability to Export Data is enabled from the settings page can you export from the Item Details page of the service?
To answer your question about ensuring export is enabled when creating a survey, the export capability is managed by the service and not Survey123.
There is not an option in the Publishing Options in Connect that will allow for enabling or disabling export it will be enabled by default.
When publishing from the Web Designer there are no publishing options like there is in Connect, but by default the root feature service and the stakeholder view will have the ability to extract enabled. The fieldworker view will not have the ability to extract enabled.
Please use this link for reference regarding the fieldworker and stakeholder views: FAQ: What are the Fieldworker and Stakeholder hosted views used for in Survey123?
Thank you,
Zach
Thank you,
Zach