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Since it's targeted at businesses and not consumers, word of mouth has been powerful for me. I've rapidly grown in the state of Michigan thanks to a few very enthusiastic operators.
I also went on a slate of podcasts last year to talk about (read: promote) my product. Podcast hosts are always looking for guests, and most of them didn't cost me a thing.
It's also been helpful to be a Google Developer Expert for web extensions, the Chrome team interviewed me and that gave me a platform to talk about what I was working on[2].
The simplest way to grow it is to share the link to it in this thread – you have eyes on you, take advantage of them.
But same SEO strategy of building lots of content still works
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.
I grew it by adding features that people would ask for on the site's forums, for example a user would say "hey can we have x feature?" and I would respond saying "great idea, I added x feature to my extension y!" This was very effective and over time others would start responding saying my extension had whatever feature they were asking, capitalizing on how relatively slow companies are to implement features.
This does rely on the extension having a site it operates on and having a forum for users though. If I were to do it today I'd focus on finding places where my extension's users concentrate, Discord, a community Slack, or otherwise, and doing the same thing.