No one is taking these discord chats and updating FAQs with them

Why do you think this is, though? This really hasn't been my experience, people are usually pretty quick to add shit to the FAQ if it actually comes up ime.

You're also relying a lot, ironically, on Google, when you advocate for using search engines as a repository for forums. Google is not that good anymore, and most forums don't come up. For a niche software, do you think the specific forum for that software would actually come up 99% of the time, or would the results just be flooded by a bunch of youtube tutorials and posts to random subreddits and other forums about irrelevant shit that you weren't looking for? If you were even lucky enough to get results in the first place, that is. Partially this is due to things moving to discord, but partially it's due to Google having an effective monopoly on search engining.

If you're just going to like, go to a forum and use the forum's internal search. One, it probably sucks because they always have these stupid idiot rules like no common words and it has to be in a range of 4-40 characters and no symbols, shit like that, which sucks. But also, you can do the same thing with discord and just navigate to the web version and then just look up what you wanted to find on the chat logs and read an old conversation. They seem functionally pretty similar in that respect.

Moderating a forum to protect against random people spamming you with CSAM attacks is also more time-consuming for a small developer, and it's also time consuming to redirect people to previous threads when they inevitably come in and post shit that's already been asked about, which is also going to breed probably a more insular culture than discord, as impossible as that might seem. Again, you're also waiting like 2 days for a response, and this is especially stupid when you're dealing with a back and forth, because not everyone is going to put in the effort to present their problems as thoroughly as possible and present you with like an actual bug report or screenshots or anything. They might not even know what to search for or ask about, and then they're completely fucked. It's easier to manage discord because of it's more active nature.

Basically, the problem is this: Forums put more responsibility and onus on the users to adequately present their problems in a more easily parsable format, and better search for solutions to their own problems. It's not a mystery, then, why people might prefer to use discord, in my mind.