Example list query: https://en.wikipedia.org/w/api.php?action=query&list=search&srsearch=eistein
Note the "searchinfo" JSON object that's returned inside the query object which contains metadata like number of search results, and the search suggestion.
Example generator query: https://en.wikipedia.org/w/api.php?action=query&generator=search&gsrsearch=eistein
The searchinfo is not there, and we need it so our users can get the "did you mean" suggestions. :-(
There should be a single API that one can hit to do this. You can combine list=search and generator=search into a single query, but given that you get two sets of results back (unless you explicitly request only one, then discard it), this feels like a hack. We should have a proper solution.