How to get Siri to read result from the web
AFAIK, you can use Siri to speak screen when the results are open in Safari, or when it shows specific excerpt from Wikipedia or WolframAlpha etc. for say, word meanings or definitions. 

For the results in the overlay, it seems not possible to me. 

I search using iPhone's spotlight and then use "search the web" at the bottom in case I need more results. 

You can look into setting up a automation for opening safari and reading it out aloud.