Given that other Discourse-based forums work fine, I would guess it's something the website does. I doubt Discord and Slack hardcode every single website in existence.
I assume that this is the Swift forums fault because no other discourse forum behaves this way, and there's (probably) nothing wrong with Slack or Discord's link embeds.
Could it be possible that the logo is so big that it's displayed as if it were a primary image, or maybe something similar to that? Also, I don't know that much about how meta attributes work, but the ones on here seem the same to the ones on the meta discourse, leading me to think it's the image size.
Specifically, both Discord and Slack use oEmbed to get information for their embeds. Do you know if the forums support this, and if they do, whether or not it supplies the logo as a thumbnail url or a photo?
Edit: They both also support Open Graph as well, that may also be a source of the information
In that case, is there any reason it needs to be the size it currently is? Would it be okay if it were resized to about 350x350 (the size of meta.discourse's logo, which appears small in both applications)?
This is a bit dated, but I figured out the reason — <meta name="twitter:card" content="summary_large_image"> property that is to blame.
Indeed, https://forums.swift.org (unjustifiably) has this very meta tag in its HTML code. In contrast, deep links like this thread have another tag, <meta name="twitter:card" content="summary">, which makes a rich embed a little more humble.