In ancient Judea, people generally spoke a language called Vulgar Koine.
This just isn’t true. Koine was a basic form of Greek, so it wasn’t the native tounge of many in Judea.
The Gospels, as far as evidence suggests were written in very basic Koine Greek (that is to say there is no compelling evidence to suggest any of them were originally written in Hebrew - and John, if you consider that a Gospel, was most certainly written in Greek). Read the Richard Lattimore (the man who best translated the Iliad in English) New Testament to get a general idea as to how it may have come across. Koine (which is the simplification of Greek, I think you may be confused on this point) was pretty much not a big deal to most people, as it was kind of an international language - and anyone who used it probably had some decent education (but there is no reason to think Jesus knew it nor is there much reason to think of him as some type of simpleton -Matthew, the tax collector, however it makes sense he would have some familiarity with the language to write a basic Gospel)
Jesus was from Galilee, so he he spoke Aramaic (there is no reason to think otherwise). He was also literate enough to read the “non vulgar” Hebrew Scriptures… now as to whether or not he was reading the *Septuagint may be a valid question, but I don’t think he was - and I think that is the mainstream scholarly consenus on that point(?).. even so point being even if it was the LXX (which was written in Koine), it was not considered “vulgar” reading by anyone. It was held in very high esteem.
Moreover, so far as we know, Jesus had very little contact with Romans, particularly “elites” (just the trial maybe, and he said very very little there anyway) - as was the cast for most people in the Empire. And those he came into contact with were probably used to dealing with a plethora of people (such as arbitrators and soldiers), so in any case his accent would not have been a surprise to anyone.
Moreover: he was from a line of carpenters - so that is kind of “middle class”. And he talked to people of all stripes (from the very high to the very low) in Judea on a regular basis, as well as perhaps to Romans of authority (such as the centurion, and perhaps he was interesting enough to garner the attention of Pilate’s wife). Something to consider.
All this begs the question - what the hell would it matter how anyone sounds to some hipster fashionista that he simply wasn’t concerning himself with anyway? I hate to psychologize, but I suspect you have an ulterior motive or point to be made. If so please spell it out.
Sum up: In order of the probability of languages Jesus knew: 1) Aramaic 2) Hebrew 3) Greek. If he knew koine Greek, it most likely wasn’t his primary language, but not many higher ups would have cared as most people in the area weren’t good at it and it was just a language “to get by” in anyway. If anything was going to come across as extermely simplistic to the learned, it would may have been the Gospels not the actual man, who seems to have been pretty accesible to people of all stripes with his inherent “cultural” mannerisms.
*I understand there was no THE LXX- but the point still holds