Chossid: “So from all the above, we see that sleeping in the sukkah is not an mitzvah deorysa rather if you’re going to sleep you should do so in the sukkah because תשבו כעין תדורו. But you’re מקיים מצות ישיבת סוכה בשלימות even without sleeping”
And exactly the same is true of eating! If you’re not going to eat a shiur of bread you are still mekayem the mitzva of sleeping in the sukkah bishleimus. But if you eat a shiur and you eat it outside the sukka you are being mevatel a mitzvas asei. And if you sleep outside a sukkah the shiur of sleeping, which is even the smallest amount, you are mevatel the same mitzvas asei.
“So we see from here it’s a question of chumrah to sleep in the sukkah. Whether you should be makpid or not to be machmir, even though you have reasons to be exempt.”
It is not a chumra! It is a halocho mefureshes despite all the twisting and turning you claim your rebbe did in this matter. To be exempt you have to have a VALID reason to be exempt, and the Rema searched until he found one. And the reason of having tzaar because you’re not having tzaar is not considered valid by anyone who is not a brainwashed lubavicher. I repeat: NO ONE!
“So I don’t get why people are having a problem with the Rebbe justifying a minheg, Aderabeh the Rama doesn’t seem to accept to just like that, rather finds away to justify it”
The problem is that the Rema’s justification fits in with the sevoro of תשבו כעין תדורו as brought in the Gemoro. Your rebbe’s justification does not, and it would have been better had he left it as a minhag without empty rationalizations.