It should not be.
Shemini Atzeret follows Sukkot but stands apart
Britannica defines Shemini Atzeret as the festival that takes place on the eighth day of Sukkot and notes that it is treated in rabbinic tradition as an independent holiday even though it immediately follows Sukkot.
That distinction matters because the day is not merely "extra Sukkot."
It has its own mood and observances
Britannica notes that the shaking of the lulav and etrog no longer applies and that the day includes Yizkor and a special prayer for rain.
This shift gives Shemini Atzeret a quieter feel than Sukkot. The harvest festival gives way to a more inward day of assembly and transition.
Its position helps explain Simchat Torah
Britannica explains that in Israel and Reform usage Shemini Atzeret coincides with Simchat Torah, while outside Israel many Orthodox and Conservative communities observe Simchat Torah on the following day.
That is why the two holidays are often blurred in popular description even though they are not the same thing.
Why it still matters
Shemini Atzeret still matters because Jewish calendars often preserve nuances that broader public memory flattens. This day holds onto the difference between closure, assembly, and celebration.
The shortest accurate answer
Shemini Atzeret is the Jewish festival that follows Sukkot on the eighth day, treated as a distinct holy day and associated with assembly, memorial prayer, and the beginning of the rainy season's liturgy.