John 12:9 begins with "Now a great many of the Jews knew that He was there".
Clarke's Commentary says of this verse:
John, who was a Galilean, often gives the title of Jews to those who were inhabitants of Jerusalem.
John frequently uses "the Jews" to refer to specific groups of Jews, usually the leaders in Jerusalem.
After these things Jesus walked in Galilee; for He did not want to walk in Judea, because the Jews[fn] sought to kill Him.
fn: That is, the ruling authorities (NKJB)
— John 7:1
Notice that in verse 13 John says "no one spoke openly of Him for fear of the Jews", even though the "no one" refers to people who would have been Jewish themselves.
Much of John 7 refers to "the Jews" and "the people" as opposing forces, even though those people were Jewish.
The Living Bible translation of 7:15 actually says "The Jewish leaders", when most other translations say "the Jews".
John refers to Passover, Pentecost, and Tabernacles as "feast of the Jews", but omits this same expression for "Hanukkah" (John 10:22).
This usage seems backward, as Hanukkah is strictly a non-biblical Jewish feast, while the others are biblically defined feasts:
… The feasts of the LORD, which you shall proclaim to be holy convocations, these are My feasts.
— Leviticus 23:2
Clearly these holy feasts are God's and, unlike the non-biblical Hanukkah, not Jewish.
For instance, in the future, gentile nations will be celebrating the Feast of Tabernacles:
And it shall come to pass that everyone who is left of all the nations which came against Jerusalem shall go up from year to year to worship the King, the LORD of hosts, and to keep the Feast of Tabernacles.
And it shall be that whichever of the families of the earth do not come up to Jerusalem
… they shall receive the plague with which the LORD strikes the nations who do not come up to keep the Feast of Tabernacles.
— Zechariah 14:16–18
Numbers 29:12–34 describes what is required during the 7 days of Tabernacles.
This includes the sacrifice of seventy bulls.
The Jewish Talmud (Sukkah 55b:9) says:
Rabbi Elazar said: These seventy bulls that are sacrificed as additional offerings over the course of the seven days of Sukkot, to what do they correspond?
They correspond to the seventy nations of the world, and are brought to atone for their sins and to hasten world peace.
The gentile nations of the world will celebrate God's festival (not the Jew's).
So why does John label only those three specific feasts as "feasts of the Jews"?
The difference is that only these three feasts require a pilgrimage to Jerusalem.
They are the feasts that would have been presided over by the Jewish leaders at the great temple in Jerusalem.
They are the feasts that would have attracted huge numbers of Jews to gather together in that city.
Hanukkah was celebrated in each individual Jew's home.
God's other holy feasts were celebrated by local congregations wherever they were.
But these three "feasts of the Jews" were, until its destruction in 70 CE, celebrated at the temple in Jerusalem.
And John consistently uses "the Jews" to refer to the ruling authorities at the temple.
This was largely taken from:
John's Gospel and the Feast,
which explains all this in far greater detail.