Umlaut modifies how a letter is pronounced; diaeresis tells you where a new syllable starts. I'm not sure how to pronounce "u" or "ü" in Turkish.
The problem with naive is that it's not very clear how to pronounce it: it's "na-ive", which isn't very clear. With naïve there's a clear indication that the "i" starts a new syllable.
While I agree that diaeresis in English are more archaic than not, I don't agree it's better style to leave them out. Right now there is, in my opinion, no good way to spell some words: "cooperation" is ambiguous (coo-peration, coop-eration, or co-operation?), "co-operation" looks ugly and is an abuse of the hyphen, and "coöperation" is nice but rather archaic.
A bit of effort to reduce ambiguity and match spelling and pronunciation (as far as the language allows) doesn't strike me as a bad thing.
I wonder if this is the impact of technology. When written by hand, there's not much practical difference between naive and naïve. With English typewriters and English keyboards, writing naïve is tricky so people, presumably, just didn't bother. Now, however, a lot of written text goes through spelling correction so, if the spell checker wants naïve then it may automatically change it or suggest you do.
In my completely rigorous and scientifically valid testing of this assumption: Word corrects to naïve, Chrome text box flags naïve, Edge text box is happy with both and imessage suggests naive. So bit of a mixed bag.
The façade of your rôle in the naïve crusade against Türkiye's self-determination will not last for an æternity, my friend. You'd better update your résumé!