No one ever ate in the sukkah on shmini atzeres, the reason chassidim (which I am noheg) (it’s not limited to Chabad chassidim) do it is because of ספיקא דיומא whereas litvaks don’t consider it.
Okay… what??? Let’s break this down:
The Gemara (Sukkah 47) brings a machloles what should be the behavior on Shemini Atzeres in chutz laaretz, and the halacha there is:
מתיב יתבינן, ברוכי לא מברכינן
We sit in the Sukkah, but without a bracha.
Rambam rules (Hilchos Sukkah 6:13): Nowadays that we have two days of Yomtov, we sit in the Sukkah for eight days. On Shemini Atzeres we sit in the Sukkah but don’t make a brocha.
Shulchan Aruch (OC 668): In chutz laaretz we eat in the Sukkah by night and by day due to sefeika d’yoma, but don’t make a brocha.
Tur rules the same, but adds: “Some have a custom to eat outside of the Sukkah at night and in the Sukkah by day – ואינו מנהג.”
Mishna Berura: The custom on Shemini Atzeres is to leave the Sukkah after the day meal, but if one wants to eat again, even bein hashmashos, it must be in the Sukkah.
Despite all classic halacha being clear that one must eat in the Sukkah on Shemini Atzeres, the custom of many chassidim based on a mesorah they have from the Baal Shem Tov is to not eat in the Sukkah in Shemini Atzeres. (Chabad does *not* follow this minhag, they only eat or drink in the Sukkah until Shemini Atzeres ends.)
Of course, after this minhag developed, chassidish poskim have built some sevoros to rely on, but the fact remains that this minhag has weak halachic basis, and is done purely due to the Baal Shem Tov’s mesorah.
The Chabad minhag of not sleeping in the Sukkah, while also being due to the mesorah from the times of the Baal Hatanya – has much greater halachic basis, since it was already mentioned as an acceptable minhag in Shulchan Aruch (albeit for different reasons).
My point is not ch”v to attack the chassidish mesorah. My point is to question why you, and many others, fixate on the Chabad mesorah not to sleep in the Sukkah (which was already permitted in Shulchan Aruch) while ignoring the rest of the chassidish velt that eats outside the Sukkah on Shemini Atzeres (without basis in Shulchan Aruch).