Tags are a way to help spread the microblog or thread type into the fediverse and searchable as well. While on mastodon, I can see a microblog or thread post type of article, link, etc, it'll show the tags, but the posts do not appear in the same tagged way a post from mastodon with a tag does. I think this is a bug for now.
If you are on a Mastodon instance and follow a kbin.social user for example, you will see their posts and comments to on kbin and can interact still on the same thread in kbin for example.
They are more of a concept coming from mastdodon type of posts.
But currently there are no lists or possibilities to subscribe to them here.
So you/we can use them and navigate but with certain limitations.
For my liking kbin is lacking lists so that not all follows have to be seen mixed in a single place.
In such lists if they existed it would be awesome that there could be subscriptions to both communities and tags.
True, but I think they make it easier to find posts originating here on kbin using say Mastodon.
There is also a difference between Posts and Articles here which I haven't fully fathomed - I think perhaps articles are more Mastodon compatible, while posts are more aligned with Lemmy... But hopefully somebody more enlightened will provide more detail and/or correct me there!
Tags are essential in the Fediverse because there's no algorithm here. No "suggested" follow or posts. Post ( I'm talking about microblogging mostly) appear in chronological order solely. So if you want to search for toots/posts/microblogs of an specific topic, or connect with people that share a similar interest with you (outside of communities/magazines/groups), tags are the only option.
You're confusing something. Hashtags matter because there is neither a global nor an instance-level full-text search on many platforms (especially Mastodon), only one for your own "storage" (timeline, favs, bookmarks, boosts). Lemmy and kbin have an instance-level full-text search, though.
As long as one person follows the author or discovered a post, it becomes visible via its hashtags to everyone on the same server. That's why you receive a warning if you write an unlisted post with hashtags, since they wouldn't work.
What you refer to as algorithm would be applied afterwards. It would collect, sort, filter, or transform those discovered posts according to settings or a generated profile (another algorithm).