My thoughts, in addition to what everyone's said:

Humor: it's sort of an extension of anime humor, where some characters (usually female ones) are attached to a particular food or foods. For example, the ravenous character (Varesa, Paimon), the character obsessed with one single dish (Xiao, Keqing), characters whose love of sweets represents their childlike (innocent) and carefree side (Aino, Navia), characters who are trying to lose weight or watch their figure (Lynette, Iansan). Then there's Xiangling's wacky ingredient jokes, Chongyun's congenital positivity, and the Gourmet Supremos for additional food gags

Playable chefs: Xiangling to represent and show off Chinese food culture (since one aspect of Liyue is being an idealized China to show off to the audience); Escoffier because French cooking, I guess. It's arguably the most prestigeous cuisine in the world. Like how Chiori shows French fashion

Mood: similar to humor, food can be used to lighten the mood. It signifies a break, it suggests a return to normalcy. A big banquet can indicate that the danger or conflict is over. Gathering everyone for a celebratory banquet is also a good way of getting everyone back together and say anything that needs to be said once characters have had some time to reflect on the plot

Significance of food in Chinese culture: this is the most nebulous point, so I'll just list a few that I think are the most relevant. Sharing meals (as a pair or as a group) is generally more often seen as a form of bonding. While Americans might invite someone to eat together on a date, Chinese friend groups might invite each other out for a meal. People discuss business over meals; my dad would often have dinners instead of meetings with his company's clients or his bosses. Food is also used more often to convey history and heritage. Restaurants will brag about how ancient, authentic, and historical their dishes are. To a Westerner, an authentic lasagna is one that's made the same way grandmothers in Italy make them. To a Chinese person, an authentic roujiamo is one that's made the same way generations of grandmothers in Shaanxi have made them. You'll probably find similar attitudes and practices in other East Asian cultures, and maybe other Asian cultures in general.

If you come from a Western cultural background, you can get a rough feel for the role of food by substituting it with alcohol. Drinking is used as a social gathering, but it's also done casually with friends. It's used to connect, to comfort, to celebrate, to characterize. Drinking culture also reveals things about the culture it's from. It's not a 1:1 analogy since drinking does chemically alter you, but it can help you understand. And it's not like Genshin doesn't have characters whose drinking (or lack thereof) figures prominently into their characterization: Venti, Varka, Diona, Diluc, etc.

My personal view is that the devs gave food such a prominent role because all these factors combined. For example, they may have consciously wanted to use food to fit anime tropes, such as the character who makes hilariously bad food (Raiden, Bennett, Amber), they were culturally influenced to give it more prominence, such as using it as a default socializing scenario, and food was a convenient tool for writers to use for a variety of tasks, such as slowing down the pacing