Ask HN: Is search on mobile not as important as on the classic web?

Need some more detail on this question. Do you mean search within a website, or a search engine as in Google?

In either case I would say, as a single datapoint, that search on mobile is just as important as on the desktop.

In some ways more important as I am more likely to use Google Maps on my mobile device than on the desktop, and I search for both specific addresses and the name of a business.

Broad question but say for a typical website you should expect ~30% of your traffic to come from mobile. This naturally varies on geography and site function.

From this classic search is still the most important from a pure eyeballs POV but mobile is significant and ever growing.