For https://www.checkbot.io/, I did posts on reddit, hackernews, producthunt and directory websites, and also put time into writing relevant articles that I can post links to. After the initial effort, organic backlinks and Google traffic have built up over time. Its search rank within the Chrome store is pretty good too, guessing large numbers of positive reviews helps here.

Feels like there's a lot of luck involved here as the search algorithms could change whenever, but building up good backlinks and reviews is going to help.