The thing is, that’s probably not really attributable to their immortality. After all, the Zandalari aren’t immortal, yet they’ve remained largely unchanged culturally and technologically for far longer than night elves have even existed.
It’s just that in WarCraft - and on Azeroth especially, though arguably native Draenor too - the world’s ancient nations and empires all seem to be so dependent upon one magic or another to prop up their cultural centers and foci that said magic’s accompanying attitudes and observances are baked into everything, from the mystical to the practical, meaning their societies otherwise top off at a medieval stage of development and then just sit in that paradigm for thousands of years on end, only developing further if one of the more ingenuity-driven or the titan-forged “genius” races comes along and teaches them about new ideas and higher technologies.
So peaking and stagnating in one single era of focusing on mysticism, swords, bows and arrows is really just the norm for native Azerothian races, irrespective of racial longevity. Once they reach that point they seem to settle into it long-term and generally require either the discovery of “magitech,” the intervention of foreign ingenuity, catastrophic society-wide trauma or all three to push them over the hump into thinking outside that box and growing beyond what previously elevated them to prominence.
The night elves remaining largely unchanged for ten thousand years wasn’t really so strange as to call for an unnatural causal factor; basically most comparably advanced races didn’t change significantly that entire time, immortal or not, or before then. Only relative newcomers like humans underwent significant change, because they were starting from scratch as primitive offspring of the vrykul, and even the clans of their flesh-cursed vrykul precursors who didn’t go into hibernation remained mostly unchanged the entire time, despite their cursed lack of immortality meaning they would have undergone generational turnover and replacement throughout the millennia like most races.