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.
TL;DR, probably never.
Like...it doesn't work on cats. It doesn't translate smiles.
If "nafnfowmfowl grtakkan ssshelpik" means "Temba, his arms wide" then the translation was correct. The fact that the crew mostly faileld to understand the communication is on them, not the translator.
This can also be seen in Data. Just because he can speak all sorts of languages and understand a majority of communications, he doesn't really know Riker's love of Troi because his translation matrix isn't designed for that in the same way that the ship's isn't designed to interpret intent.
You don't even need to go to Darmok to see this limitation, really. The fact that the translator provides human translations of klingon speech is not enough to understand their cultural intricacies. The same could be said of "pon farr" being a "time of mating". That knowledge alone could not have prepared Kirk for the trial or even hinted at there being a trial.
The translator is neither mind reader nor cultural liason. If it were we wouldn't have needed Troi.