Quoth the @Ijon: "Here's a relatively easy improvement: if the user types more than one character unambiguously associated with another language (relatively few cases, e.g. Hangul for Korean), automatically switch the language and search in that language."
Neat little idea. Little quality of life improvements like this often don't really move the needle, but they're also often quite simple to implement and contribute a lot to user delight. Worth considering!