They are closely linked conditions. I do not have anxiety or depression, but my undiagnosed and then untreated ADHD was causing me both conditions.
They are separate things but they are intertwined, so much so that ADHD very frequently comes with a dual diagnosis of one or more other conditions, or is confused/commingled with eg. autism. A proper assessment can disentangle them and reach the correct diagnosis.
I don’t like to call it hyperfocus because of this narrative that it is a “superpower”. It is still inappropriate focus. Barkley calls it “perseveration”, which seems more accurate to me. Yes I can get things done, but at the cost of an inability to observe time and by causing me to forget everything else, including food.
Medication has been wonderful but it isn’t perfect, and I find that it takes work for me not to overcorrect and lapse into too deep a state of focus.
As for exhaustion, I used to get that when I was undermedicated. At the appropriate dose, I’m fine. My “natural” state of perseveration of focus usually comes with much larger baggage (eg. blind panic at a looming deadline) so it’s hard to ascribe the exhaustion to the act of focusing.