Congratulations 😎👍.
The Contax IIa is a very nice camera, lightweight and silent. Wish I had had mine available several weeks ago in a Paris cafe near Gare de Lyon, instead of that noisy SLR.
Watching the video at 1/25 sec. shutter speed, something seems a bit strange to me, regarding the second curtain. Unfortunately, I'm not a technics expert and can barely decribe it. Perhaps the second curtain is a bit too fast during the first third of the window...? 🧐
Did you check out if the shutter actually opens at these high speeds? It's a common problem: The curtains run but they don't open.
I usually check it out after removing lens and the body's back: I look into the light through the mount and release the shutter. It's possible to notice if the curtains actually open - and open completely. Often, they don't open completely at 1/1250 sec.
I suppose I would let the camera have a professional CLA at one of the well-known workshops. Sure, of course it's not a Leica, but a Zeiss Ikon Contax is also a precious camera, one of the most precious in photo history.