Dear Waves,
I'm coming back to the board in a little bit.
For right now I want to comment on your word "useful."
Your post has lots of mood related descriptors -- talk of feeling crabby, feeling exhausted, needing caffeine, . . .

. . . but this concern about being useful is not necessarily related to mood issues. I wonder what that is about.
What do you mean when you talk about being useful?
Do you think that this is about your existential / situation issues? Or is it something else?
Is it something that you can re-frame /re-think so that you can feel better?
Have you defined yourself in the past as being useful to yourself and others?

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I think I do not really want or need to feel useful. But if you asked me if I like to feel "needed", I might say "yes" depending lately on what moment you you asked me.
I have spent most of my adult life trying not to want to feel needed. This is something from my childhood that I am able to drop a little bit each year as I get older.
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I do feel the need to "connect" with people. I think connect is a word for me.
At this point in my life if I could not connect with others to some degree on some level, I might be unhappy.

Is my "connect" similar to your "busy"?

I am not asking this to be difficult or give you lots of quiz questions. I'm wondering how you could feel better about yourself.

M.