After replacing a bottom bracket with square taper I repeatedly have to tighten the screws that fix the crankset (on each side) to the bottom bracket axle or otherwise I can feel sometimes a slight movement of the crankset on the axle. I understand that this might be needed once or twice for parts to really settle in but I wonder how common that is or wether there are tricks to avoid it. This is an old Shimano crankset and a new Shimano bottom bracket. Since the screws are not very long (about 10mm of thread) I also fear I could damage them in the process.
As some commenters have indicated, your crank arms are worn out.
We can speculate all day about what was the cause, but since you indicated that you felt some wobbling, that means they are now because that is the fast-track to ruining the square taper interface.
You'll have to replace your crank arms.* When replacing them, make certain that your crank bolt is tightened to spec. It needs to be pretty dang tight. Also, when you get the new crank, replace the crank bolts with the snazzy allen headed crank bolts.
*If you are short on cash or like to gamble, you could also just replace the crank bolts with the snazzy ones, then tighten the absolute snot out of the bolts. While a low chance of success, it might work. The BB spindle is hardened steel, and the cranks are aluminum, so you don't pose much risk to the BB spindle if you choose this option. But still abide by the no riding when the crank is wobbling rule.