Perhaps you should consider the full context. The feast of tabernacles is not the feast of unleavened bread.
John 7:2-3
(2) Now the Jews' feast of tabernacles was at hand.
(3) His brethren therefore said unto him, Depart hence, and go into Judaea, that thy disciples also may see the works that thou doest.
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John 7:14 Now about the midst of the feast Jesus went up into the temple, and taught.
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Joh 7:23
(23) If a man on the sabbath day receive circumcision, that the law of Moses should not be broken; are ye angry at me, because I have made a man every whit whole on the sabbath day?
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John 7:37
(37) In the last day, that great day of the feast, Jesus stood and cried, saying, If any man thirst, let him come unto me, and drink.
John Gill Commentary
John 7:37
In the last day, that great day of the feast,.... That is, of tabernacles, as appears from John 7:2, which was usually called חג, "the feast", in distinction from the passover and Pentecost (q); and the eighth day of it was called הרגל האחרון, "the last day of the feast" (r), as here: and it was a "great day", being, as is said in Leviticus 23:36, an holy convocation, a solemn assembly, in which no servile work was done, and in which an offering was made by fire unto the Lord. According to the traditions of the Jews, fewer sacrifices were offered on this day than on the rest; for on the first day they offered thirteen bullocks, and lessened one every day; so that on the seventh, day, there was but seven offered, and on the eighth day but one, when the priests returned to their lots, as at other feasts (s); but notwithstanding the Jews make out this to be the greater day for them, since the seventy bullocks offered on the other seven days, were for the seventy nations of the world; but the one bullock, on the eighth day, was peculiarly for the people of Israel (t): and besides, they observe, that there were several things peculiar on this day, as different from the rest; as the casting of lots, the benediction by itself, a feast by itself, an offering by itself, a song by itself, and a blessing by itself (u):
(q) Shirshashirim Rabba, fol. 5. 3. & 7. 3.
(r) Misn. Bava Metzia, c. 7. sect. 6. & Maimon. in ib.
(s) Bartenora in Misn. Succa, c. 5. sect. 6.
(t) T. Bab. Succa, fol. 55. 2. Bemidbar Rabba, sect. 21. fol. 231. 1.
(u) T. Bab. Succa, fol. 48. 1.
When God instituted the feast of tabernacles He did not specify that the work of cooking and preparing food was permitted as He did for ULB.
Leviticus 23:34-36
(34) Speak unto the children of Israel, saying, The fifteenth day of this seventh month shall be the feast of tabernacles for seven days unto the LORD.
(35) On the first day shall be an holy convocation: ye shall do no servile work therein.
(36) Seven days ye shall offer an offering made by fire unto the LORD: on the eighth day shall be an holy convocation unto you; and ye shall offer an offering made by fire unto the LORD: it is a solemn assembly; and ye shall do no servile work therein.