I had several images get stuck for hours or even days on:
“Analyzing image. Image will not be visible to other people while analysis is in progress.”
I tried different things, but what worked for me was surprisingly simple: increase Sharpness by just +1.
The difference is barely noticeable, but the image uploads normally after that.
I use XnViewMP to increase the sharpness and save a copy of the image. I keep the original unchanged and upload the modified copy to Civitai.
I tested this on different images, and so far Sharpness +1 has worked for me every time.
I don't know if this is a real fix or just a workaround, but it might be worth trying if your image is stuck in “Analyzing”.