I had no idea Twitter’s search updated their index immediately after a comment is posted though.

While I never had a Twitter account, it's the major reason that I used the service anonymously. In an unfolding event, like a natural disaster or something, it was absolutely unparalleled in its ability to rapidly comb through enormous amounts of information being plonked in by people around the world. I strongly prefer Reddit-style forum structure most of the time, but for issues for which there is no pre-existing communities and where the common issue is one that will only exist for a short period of time, I think that Twitter's ad-hoc connections between retweets and hashtags works much better than Reddit's association-of-comments-by-subreddit. I understand that Mastodon, unfortunately, doesn't have a full-text search feature, just searching based on exact hashtags. Actually...hmm. I was just talking about Kagi's search lens for the Threadiverse in another comment that I saw. I wonder if Kagi actually indexes Mastodon as well? That'd provide for similar functionality.

investigates

No, it looks like they only do the Reddit-alike Threadiverse (lemmy, kbin, mbin, etc), for which they use the term "Fediverse Forums".

investigates further

It does look like they index in real time, though, or at least quickly -- they probably are one of the institutions out there with an instance slurping up everything out there. I was able to find your comment on that search lens.

That’s a lot of updates considering the amount of posts they get daily.

Yeah, I'm sure that however the Twitter guys built it, they specifically designed it around permitting inexpensive index updates.