wow, searching the thread is a nightmare. there's a non-native search panel that comes up with cmd+f, and you press cmd+f again to do a native browser search... and both of them don't actually search the thread, only the visible section. you have to scroll around to load all parts of the thread in order to actually search the whole thing, with either of the two searches!
Discourse's own search, the one that comes up first, is definitely supposed to search the whole thread, that's the whole point of it. Discourse does a lot of loading/unloading the page as you scroll on these big infinite-scroll threads so the native browser search would be not so useful, in the way you describe.
I don't notice the Discourse one having any trouble searching the whole thread as advertised here though.
