The key word here is "connected" instances. You don't find hashtag-related posts from all the servers, just the servers that your server is connected to and also only posts that your server has seen from other servers.

This is why, on my instance, I relay with over 300 other instances, some of them are the larger ones. All the posts they see on their server are duplicated onto my smaller server. The impact is that while my server is small, it has the same messages as one of the large servers which makes for a better experience. Note that Mastodon.social does not relay with any other instance. Not that most instances could possibly hold all their posts and accounts anyway.

When I search for hashtags on my instance, I do get a lot of hits.

Many smaller servers do not relay as much as I do, or at all, because it requires disk space to store all the posts, images, and accounts that are streaming in constantly from all these other servers. I don't have these concerns because I have unlimited capacity. So, the experience will vary depending on which server your account is on.