Step 2 - picture number 3 is wrong, I broke off a little part of my PSP E1004. The left arrow points up but you have to pull it down, while trying to pry gently to the right. I learned the hard way after I managed to take it off.
Pro tip: If the button works properly and you only need to fix 1 axis, you only need to remove the 3 pins that holds the potentiometer. You can snap off the potmeter from the metal casing of the stick and replace that part only if you have a compatible one but you need to be carefull, as there are multiple size of analog sticks with different potmeters on the sides and sometimes the shaft doesn’t match. But if you have multiple spares analog stick you can try to find a matching one.
I’m missing many screws mentioned, also, the two side pieces can’t be slapped off without unscrewing a couple of security torx screws on the side where the HDD was. Maybe this is not on every iteration but it’s important.