and not a middle eastern man
The racial composition of those areas was completely different in our Lord’s time. There were plenty of Greeks (+Phoenicians) and Romans everywhere and Jews weren’t exactly by today’s standards ‘middle eastern’. What you call ‘middle eastern man’ is rather a modern mixture of races (I do not need to remind you of the Muslim conquest of those areas in 632 - 661 and then by the Abbasids in 750-1258).
We know that He was not pale, but He also wasn’t a black man. We know that He had a beard and slightly long hair. He was not obese and was probably relatively muscular (because he worked as a carpenter in early years). These main characteristics endured the trial of time, probably passed on verbally by the first Apostles and their direct successors (who in human ways had the same question as you and all of us) until, in the early centuries of Christianity, they began to be immortalized on walls/Icons. However, when those who remembered Jesus or remembered-those-who-remembered-Jesus passed away, some deviations from his image could normally begin to appear.
Don’t be afraid of depictions. So what if European art movements (like Renaissance you mentioned) influenced many paintings? In the same way Asians preferred to show His Countenance with —understandably — Asian features, and in Africa, you can find images of black Jesus. Does
every (human-made) depiction is true? Probably not. Does this matter for our salvation and our veneration of Lord’s Countenance on those images? Definitely not.
But anyway, you asked about the real/miraculous images:
Does it even seem plausible that he would leave us an image of his face when he wants us to have faith?
The
article posted by @(name removed by moderator) gives a fair insight into this question.
I would also add to this list a
painting (Divine Mercy Image) which Jesus literally Himself ordered St.Faustina to paint (she asked Eugeniusz Kazimiriowski to paint it exactly as Jesus told her to).
“I promise that the soul that will venerate this image will not perish,” — Jesus told Faustina, according to her diary, which has been studied and authenticated by the Catholic Church over several decades. Although made by human hand, I wouldn’t dare to deny its authenticity and its creation according to will of the Lord and with His help.
I’d say don’t worry and trust the images and Icons you see. Especially those miraculous — since the Holy Tradition of Church tells us about their authenticity.