Not OP, but I struggle with Discourse search, both in terms of usability (not quite good) and presentation - both D. itself and it's search is made by someone who doesn't need to exchange information and persist it. After some attempts I just fallback to external search with 'site:domain.tld search term'.

Wasting 90% of my screen real estate while actually hiding useful information isn't helping too.

Oh, that's disappointing, but it answers the question of how the market is defined for the quoted statistic.

Yeah so it's not 34% of the discussion market, it's 34% of the top one million sites that use a discussion platform. The distinction is important, because the top one million sites are likely to be run by corporations as product Q&A platforms, which is very different from what you want from a Google Groups clone.