Hi Maximillian,
After looking at your video, I understand that the upper parts don't have any connection to the grey sheet-metal part.
May I suggest a workaround where, there is a very thin, transparent 1mm wire touching the two surfaces so that you can model the animation to stop the upper part at the edge of the wire, touching the sheet metal surface? It's a bit of a dirty fix but might help if you are only interested in animating the assembly.
Regards,
Lucky