In my experience the input field lags on short chats too, sometimes in the middle of writing the second or third prompt. Are they running some kind of prospective evaluation or something?

When you are writing completely new prompt - it sends every character to server when writing and tries to make suggestions based on that.

And keeps doing it in intervals in /prepare endpoint, during each prompt.

So if you are working with something sensitive - don't write it to browser directly and edit it there.