Hi there again and sorry for my late reply.
I actually solved my problems, and it was in fact due to one single plugin. Here's how I did it, it may be helpful for others:
I removed all plugins from the components folder starting with the letters A to C. Then D to F, and so on. After I removed all plugins from M to O Logic suddenly behaved as it should. I then isolated the letter N. In there it was a plugin based on the Nebula-technology from Acustica Audio, namely the just updated Taipei from London Acoustics. After removing the plugin from the songs and then reinserting it (I have this wonderful tape machine emulation in all of my songs as the last one in the mixbus) everything went smooth.
Since then I didn't have a single crash or strange behaviour and am happy with my new setup and the Mac Studio.
About me not being able to find the Hornet VU meter: It was indeed in the other components folder on the HD, as the only plugin in there. Strange stuff.
Oh, and about the little display when Logic is loading a project: It still just shows me Klopfgeist. I wonder why's that.
Cheers, and thanks again for all your help and time.