I have setup a Form in the Web Map to capture some data. I have a date field in the form and I have set it to be a Date input type. When I use this Web Map in Experience Builder with the Edit widget, this date field (and all other date fields) do not use a date picker and I can only add a date by typing it in.
Date field setting in Configure Form:
Edit widget in Experience Builder:
This appears to be a known issue and is in the pipeline for an upcoming release. Please vote for the ArcGIS Idea below:
This is in the works for the upcoming release. This will be seen across any apps using the 4.x JSAPI editor widget.