@ILoveNumAn welcome!
While Mastodon doesn't have native groups yet, there are some other Fediverse alternatives that do. The most notable example probably is #Friendica: https://fedi.tips/friendica-a-flexible-fediverse-server-type-with-long-posts/
While I do have a Friendica account myself, @fixato@libranet.de, I don't find myself using it actively. In theory it's closer to what #GPlus is, in reality it just doesn't feel as polished, and I haven't been able to curate a home feed and 'circles' with it that keeps me active on the platform on a regular basis. The user interface and user experience of #Mastodon just feels a lot more thought through and polished.
The same applies to #Diaspora, the platform #GooglePlus probably took the whole idea of Circles from, where they are called "Aspects". There's also #Hubzilla, which has even more features, but which just felt slow and cobbled together. I would suggest you give them all a try though, as your experience and needs might differ from mine!
Now, having said that Mastodon doesn't have native #groups yet, there is some third party support for them in the form of #Guppe (https://a.gup.pe/). Check out @FediTips for a good primer: https://fedi.tips/how-to-use-groups-on-the-fediverse/
Mastodon 'recently' did add a feature that reminded me of the early days of G+, which should help you discover people a bit easier than manually trawling hashtags, and that's the ability to follow a hashtag, so its posts will automatically appear in your home feed.
Finally, if you like the overall interface of Mastodon, but miss being able to format your posts by wrapping words in asterisks, underscores and the likes like G+ supported (though with less frustrations imho), or write posts longer than 500 characters (like this one), then I would suggest you also check out #GlitchSoc, a fork of Mastodon that adds a bunch of features which Mastodon for example itself has shown a resistance to to add. https://glitch-soc.github.io/docs/
Best advice I can give is to just try out several different alternatives and then settle on the one that best suits your needs. :)
Anyway, I hope this wall of text has been of some help. 