Does the Talmud talk about a food fight (i.e. throwing food at one another)?
In general, what would the Talmud have to say about a food fight in terms of wasting food, or otherwise? Is it okay? Not okay?
There is something like you mention in the Talmud Yerushalmi in Demai 7:1:
Rebbi and Rabbi Yossi were invited as guests to eat at the home of a certain man. However, the Rabbis suspected that he did not properly tithe the food being served, and they wanted to attempt to tithe the food secretly. Their suspicion was noticed by another man who told the owner to look at what the Rabbis are doing. Once the Rabbis realized that they were under scrutiny, they started throwing their food at one and other in a playful manner and by doing so they were secretly tithing the food.
דא"ר שמואל בר רב יצחק רבי ורבי יוסי בי רבי יהודה נתארחו אצל בעל הבית אחד אזל לישנא בישא א"ל הב דעתך דאינון מחשדונך יתיב לי מעייני לון והוון עבדין נפשין מזרקין אילין לאילין ומתקנין
As far as wasting food, right before this incident the Talmud dismissed the notion that this is considered wasting food because he can make the tithed portion into tiny pieces less than a כזית and it is not considered wasting food.
רבי ירמיה בעא קומי רבי זעירא ואינו אסור מפני אובדן אוכלים א"ל מפררו כל שהוא
I found one mention of throwing food in the gemara - but in general there is a law not to waste food and thus the whole idea of throwing away and spoiling food goes against the Torah ethic.
The gemara in Shabbat 105b brings a story of Rav Sheshet who threw small fish on his maidservant’s head to instill fear in the members of his household by pretending to be angry. The Sefer Hachinuch (#529) comments
Nonetheless their supervision would always be over them, that they not throw down something that would be destroyed by this.
This is because there is a general prohibition of bal taschit, not to destroy unnecessarily. This is based on Devarim 20:19
When in your war against a city you have to besiege it a long time in order to capture it, you must not destroy its trees, wielding the ax against them. You may eat of them, but you must not cut them down.
The Rambam codifies and extends this (MT Melachim 6:10)
And not only regarding trees, but even one who destructively breaks vessels or rips up clothing or tears down a building or seals up a spring or wastes food violates the Negative Commandment of “Do not destroy”.
The Talmud in Berakhot 52b mentions the importance of not throwing away bread larger than an olive-size piece
And Beit Hillel say: If the attendant is a Torah scholar, he removes the crumbs that are an olive-bulk from the table at the end of the meal and leaves only crumbs that are not an olive-bulk, as food that is less than an olive-bulk is not considered food and there is no prohibition to ruin it.
There is even an opinion in Shabbat 140b that eating bread of higher quality, when not required, is waste, although that opinion is not upheld
And Rav Ḥisda also said: One who is able to eat barley bread and nevertheless eats wheat bread violates the prohibition against wanton destruction. One who wastes resources is comparable to one who destroys items of value.
In light of all these statements it is quite clear that throwing food at each other and spoiling it doesn't go in the spirit of the Torah and doesn't teach the proper attitude. See the Sefer Hachinuch at length on this.
שלא לנהוג בזיון באוכלים
ואין זורקים הפת משום בזיון אוכלים וכשם שאין זורקין את הפת כך אין זורקין אוכלי' הנמאסים ע"י זריקה אבל מידי דלא ממאיס כגון אגוזים ורימונים וחבושים שרי:
One should not do disrespectful things with food.
One should not throw bread, because it is disrespectful of the food. And just as one should not throw bread, so one should not throw any food which will become repulsive [spoiled] by throwing it, but something which does not become repulsive, such as nuts, or (hard) pomegranates or quinces, may be thrown.
Bread requires a higher level of respect, and one should not throw bread even if it will not become spoiled by throwing it.
An additional source in the Talmud is an incident mentioned in Ta'anit 24b where Rabbi Yehuda saw two people throwing bread, which upset him to the extent that a famine occurred.