yeshivishsocrates — “in kabbalah, the right side represents midas hadin and the left represents midas haracham”
I think this is incorrect. The Sefira Chessed is on the right side, the Sefira Gevura is on the left side.
This is why we find many times in Halacha/Shulchan Aruch that the right takes precedence over the left (e.g., putting on shoes, etc…)
As for the reason why the buttons are switched on shirts for Chassidim; it stems from a halacha in Kitzur Shulchan Aruch, 3:2 and ibid not to replicate the styles of the non-Jews.