We are already strongly off-topic. You asked about SSO logins, and ActivityPub is not related to that in any way, just as little as the protocol through which emails are sent or what an RSS feed is. Similarly, the entire Fediverse, including Mastodon, is based on the idea that you only need to join one server. In other words, if you federate a category or tag, a Mastodon user doesn’t even know where the traffic is coming from in principle; it just appears in their feed if they have subscribed to the traffic moving through the ActivityPub you offer.
So, we have moved from login options to the basics of federated systems.
Searches do not work that way. Most likely, the user’s Mastodon server doesn’t even know about the existence of your forum. The situation changes on that server when someone there starts following a category or tag from your forum, but they must first know the identifier your forum uses through other routes, or you can think of it as an address.
After that, the information begins to spread slowly, and more quickly by the actions of someone following your forum to their own followers if they share it further.
Finding becomes easier when Discourse learns to use hashtags (and agrees to communicate with Friendica, which is the Fediverse’s equivalent to Facebook), but we’re not quite there yet.
So it’s about two things:
- ActivityPub is like RSS and doesn’t do anything by itself unless someone knows how to read it
- the entire Fediverse is based on the idea that those elsewhere never need to come to your forum
Spend some time here. It may help to understand the very basics of what federation and Mastodon are, and what they aren’t.