Language is not about just grammatically correct sentences, it’s about expression, intent, and communication that goes beyond the spoken, written or even motioned word—not one of these things is in the realm of possibility for current (and dare I say even future) AI.
Your Star Trek comparison is also incorrect. Following your logic, we’ve had a “bonafide universal translator” for a while now with websites like Google Translate (and so on). But none of these websites or AI tools are capable of learning languages on the fly purely from context and with minimal input data (that’s the magic of Trek’s UT, what they call linguacode).
No, AIs have not “solved” language in any way.