помочь (при)готовить еду

Let me explain this THE. We use it when we refer to everything that logically belongs in a set. For example, if we speak of throwing a party, we know that there are certain things that every party logically has. We assume to everyone considers these to be essential parts of a party, so we treat them definitely: [Uly]: Since all five of us are in quarantine together, why don't we throw a quarantine party this Saturday?!
[Tatiana]: Great idea! I'll bring THE beer. (=every party has beer or liquor)
[Grumbler]: Ok, I'll order THE cake. (=assuming that every party has a cake)
[Uly]: I'll handle the music. (=since every party has music)

So when we hear this THE, we assume this is part of a subset. In this case, it's among the things to be done somewhere - in someone's home for example. There's THE laundry, THE cooking, THE cleaning, etc. Having said that, we would use "help with THE cooking" in a situation where, for example, an elderly couple lives alone and the man suffers a stroke. Their daughter lives somewhere else, but decides to come in each day and help with THE cooking - that particular chore among all the others. If it was just one occasion or a casual thing, we would just say "help with cooking."

In short, this post means "to help out by attending to THE (chore of) cooking (so that someone else doesn't have to do it, or at least not do it alone).

There may not be a distinction in Russian, but at least now I hope you understand in English. If not, please let me know and I'll explain further with other examples.

Всё очень понятно, Улий! 🙏Ты, кажется, прав: в русском языке нет такого чёткого разграничения.

👍🏼