Update: I confirm that coffee doesn't "push" me, as other people report. Well, it does, slightly, but that's probably more the sugar than the caffeine. My motor function isn't influenced at all.
But apparently, coffee affects my mood in a positive way. It doesn't fix tiredness, but at least I don't get a headache from it any more. It doesn't boost my brain activity, but it makes me worry less about irrelevant things, so it indirectly helps me focus.
Some people describe that coffee turns them into a "zombie". I think this applies to me a bit. As a zombie, I do what needs to be done. As a human, I keep pondering about my life, which doesn't lead anywhere.