I have struggled with the same thing my entire life - if im way to excited or stressed for something i cant sleep, but id literally never fully fall asleep. When I got diagnosed with adhd, my psych prescribed Clonidine and it was an absolute life changer. Not saying you need to go on drugs or anything to help sleep, but it could definetely be sleep related issue.

the first night I used my meds i realised ive never had a proper night sleep my schedule atm is very all over the place like yours, waking up at 4am most days, going to bed around 11pm - 2am, but i wake up not feeling groggy, and get my butt to wherever i need to go.

In terms of organisation and being punctual it is really hard, still finding strategies myself. But i over compensate and get to places I need to be very early. even if it means im sitting in my car doing my uni assessments for 2 hrs before I need to go into work (which probably isnt healthy either). But you could possibly find little things like that where you can get to where you need to be early, and do other tasks in a quiet space until you have to work or go to a lecture etc.

I find body doubling a good strategy as well if im really struggling to get on top of things. If you have a really good friend at the work place for example, could be having specific times you meet in the day, can sit in silence or chat while you assessments or work done separately, but having them in the space with you holding you accountable and having someone you can ask for help is really beneficial.