I tried it with a bunch more magic links on my sandbox. For reference, the source of the comment is as follows:
[chat] [ask] [answer]  [faq] [meta-faq] [faq#flagging] [physics.se]
This is the result. The title-text of the
[chat] link is broken, and most of the link targets are borked.
(I can't use
[meta] on the formatting sandbox since it's on meta, but here is the result of quoting a comment with meta on it on main)
Looks like chat treats the magic links in the quote as if they're chat magic links, which work differently.