I’m trying to figure out the best way to create a new version of our Election Info Lookup app. I developed the existing app several years ago using the District Lookup widget in Web AppBuilder. The District Lookup widget is excellent - it takes input from either a user typing in their address (geocode service) or from clicking on the map, and it automatically selects both the voting precinct boundary and its associated polling place (via relationship class) and shows attributes for both on the same popup. Additionally it has a routing tab that shows turn-by-turn driving directions - all in the same widget. The app works great, and our users love it. It's been suggested to us that the Near Me or maybe the Query widget could be used to replicate the functionality of the District Lookup widget, but what I can get to work with these is nowhere near as elegant. For now it looks like the only real solution is to keep using our Web AppBuilder app.
The official migration plan says to replace this widget with an entire separate web app. Why this is only available as an instant app when both use the exact same SDK and layout system under the hood is beyond me but that's the hand they're dealing. Your best workaround for now is to see if the instant app meets your needs, build it out and embed the app as a page in your experience. If that fails you'll have to plead your case in this Idea and hope someone changes their mind.
Have you looked at using the Zone Lookup Instant App? I haven't used it myself but that's listed as the suggested replacement for the District Lookup widget in the Experience Builder/Web AppBuilder functionality matrix.
As @DavidSolari and @WorcesterGTSS point out the official replacement for this widget is the Zone Lookup Instant App. It's very quick and easy to set up and can be embedded in an Experience Builder project if you want it as part of a larger site. I'm not sure if the Instant App supports directions.
Here is how you can build Zone Lookup in Experience Builder. You should be able to link this to a Directions Widget to support routing as well.