Your guide really was the reason I would even attempt to open it!
Weird that it was the exact same screw, and good idea to look for a broken A7 III. I think I will just use mine for now (and hope the sensor does not fall apart), and if I see any problems I might try that.
Thank you so much for this guide! I thought I had to replace the shutter, but when opening the camera I found that only the frame around the sensor visible in picture 3 of step 27 (lighter grey just around the sensor) was loose because the screw at the bottom had completely fallen out. As I already had the new shutter I put it in anyway, as it might have been damaged by the loose frame.
If anyone knows how that frame is called or where it could be ordered as a replacement part, I would be very glad to know! For now, I just removed it and everything seems to work perfectly.