[mothered]

I woke up at 7am naturally after going to bed at 3:30am. Though that's later than I'd get up during the week, I almost "can't" stay asleep.

As a general statement, the body needs sleep. You can only put up with 3-4 hours for ex-amount of days/weeks until you begin to shutdown, mentally.

When I'm not working, due to my Intensive computational tasks, I sleep at around 4am and awake at 9:00-9:30am. That very minute, I resume all sessions. It came to a point where I did In fact crash on the couch sometime after midnight and woke up 5 hours later, with my hands still on my laptop's keyboard.

Very true! I certainly usually need about 8 hours. Usually on weekends I get a proper nights sleep (with exception to the one just passed). I've noticed an inability to focus for long at all.

You're spot-on with this comment:

I've noticed an inability to focus for long at all.

On one occasion when I only had 3 hours sleep, I was struggling to function properly, mentally. Typos during coding, spelling errors during posts etc. I even had to take the day off work.