Check out the differences between Lev 23:40 and Neh 8:15 and their surrounding verses.
Obviously Nehemiah is from the NK but it's a curious matter. The lists are not the same ("fruit" being used in Lev, for example), and also the Nehemiah one says that they are to make the sukkot from the branches whereas Leviticus lacks that statement.
What does it mean to "sit in sukkot" (Lev 23:42)? I would imagine it is likely figurative at least in part (as it usually is), but that is a very broad scope of possible meanings.
What is a sukkah? One thing that stands out to me is Lev 23:43 saying that He caused Israel to dwell in them "in My causing them to go forth". The other example in the Torah of that wording is Ex 16:32, and presumably around that time they were living in tents (Ex 16:16). What is the distinction being made? Are they practically speaking the same as each other (sukka vs tent) or is there a non-overlapping definition? Did Israel very initially live in huts as they escaped Pharaoh and did they only acquire tents later? Is there any connection between the sukkot themselves and the list of branches and fruit, etc?
NK can't be trusted so I do not care for it and I would advise everyone to concentrate on the Torah only.
Lev 23:40 uses several terms that IMHO means branches of those trees mentioned. So I think it is basically a matter of figuring out what these words mean.
To dwell in sukkot means to live in it as you would in a tent. I.e sleeping, eating and being present there during the day as you would in your house. This is my current assessment of the verse.
Basically, from my understanding, sukkah is a shelter of branches and leaves. When I was little, I used to make those in the woods all the time. The difference between Tent and sukkah is in the materials IMHO. Tent uses fabric (i.e goat's hair), while sukkah uses leaves. I do not think Hebrews lived in sukkas when they left Egypt, however it is a possibility. I am not sure about that.
I found one verse where the word seem to mean "shelter" or "covering" - its Ex 40:3.