ChatGPT's prompt is on the order of 1k, if the leaks turn out to be real. Even that one seems a bit high for my taste, but they're the experts, not me.
>It’s logical to use the context to tell it what to do.
You probably don't know much about this, but no worries I can explain. You can train a model to "become" anything you want, if your default prompt starts to be measured in kilobytes, it might as well be better to re-train (obv. not re-train the same one, but v2.1 or whatever, train it with this in mind) and/or fine tune, because your model behaves quite different from what you want it to do.
I don't know the exact threshold, there might not even be one as training and LLM takes some sort of artisan skills, but if you need 24k just to boot the thing you're clearly doing something wrong, aside from the waste of resources.