Web app / dashboard with map featuring a region/district dataset. Survey form embedded in the web app/dashboard to capture information to populate form fields.
Users search for a locality. Once the locality is found, the user clicks on the map and has both the locality name and the region/district name populate respective fields in the form.
Is this process possible and can the question be repeated, such as, 'place I would visit first', and then 'place I would visit second'.
I do not believe it's possible exactly as you described. Pre-filling the form is done by a constructed URL with parameters, which can't be done when drawing from more than 1 feature layer. You could accomplish the 'place I would first visit' (IE: One place) by enriching your "district" dataset with another field that contains the "region" name (instead of trying to pull the respective values out of 2 different layers).
I cannot think of a way to let people pick a second place, though.
Here's one that I have embedded in a dashboard, with the "UAS Mapping (Completed)" list on the left being used to pre-fill some of the fields in the "Add New" S123 form (Could accomplish the same thing with pop-ups in that feature layer to launch in a new tab)
And here is how it's set up in the dashboard (highlighting that it's only drawing from one feature layer)
I suppose you might be able to accomplish drawing from more than one layer using the arcade expression functionality that's in there now, but I haven't ever tried.
Something that might be of use, considering you'd like to be able to click on a layer in the map and have information transferred to the form.