I have the same issue under DX11/DX12 in both Unity 2022.3.42f1 and latest Unity 6 in HDRP. It appears to be related to wrinkles. If you go to:
CC_Base_Body --> Std_Skin_Head --> Exposed Properties, all the way at the bottom is a checkbox for "Use Wrinkle". If you uncheck it, the errors will stop. But unfortunately, now you don't have the wrinkles.

Unity 6 in particular does not like whatever is going on and crashed on me yesterday trying to look into how to get these wrinkles working.

DX12: Texture index out of range
0x00007ff74720d08d (Unity) StackWalker::GetCurrentCallstack
0x00007ff747212169 (Unity) StackWalker::ShowCallstack
0x00007ff7481ff231 (Unity) GetStacktrace
0x00007ff7488b9e6e (Unity) DebugStringToFile
0x00007ff747306210 (Unity) GfxDeviceD3D12Base::SetTextures
0x00007ff747027ff4 (Unity) GpuProgram::ApplyTextureParameters
0x00007ff7472f034e (Unity) D3D12CommonShader::ApplyGpuProgram
0x00007ff7472babe1 (Unity) D3D12ImmediateContext::BindShaders
0x00007ff747305f1d (Unity) GfxDeviceD3D12Base::SetShadersThreadable
0x00007ff74893fb54 (Unity) GfxDeviceWorker::RunCommand
0x00007ff74894c18b (Unity) GfxDeviceWorker::RunExt
0x00007ff74894c2a8 (Unity) GfxDeviceWorker::RunGfxDeviceWorker
0x00007ff746f72d2b (Unity) Thread::RunThreadWrapper
0x00007ffd5a47257d (KERNEL32) BaseThreadInitThunk
0x00007ffd5aa2af28 (ntdll) RtlUserThreadStart

After further review, I’m pretty sure I know what the root of the problem is. When I inspect the head material, I can see that between all the different textures including the wrinkle maps that were up to 32 different textures. I think I read somewhere that this is a hard limit. By disabling the wrinkle maps were reducing the number of textures which makes the error go away at the expense of the wrinkles. The workaround I found for now is to simply bake to the default shaders since this reduces the textures.

Unity 6 crashing, doesn't surprise me. It crashes all the time for me even on newly created empty project...

2023.3 Shouldn't be throwing that error. What is the build platform for the project? Some build platforms have max texture limitations. e.g. Most WebGL system have a limit 32 textures at most in a shader, but can go as low as 8 textures. Also some MacOS systems impose texture limits too.

The wrinkle system uses over 40 textures. Baking the character uses a lot fewer textures and should get you under any 32 max texture limits.

Or it's a bug in Unity?

I've just tested in 2023.3.49f1 HDRP with full DXR settings and it doesn't throw this error. At least for the windows build platform.

I have the same issue. Changing to Vulkan for at least when I'm working with the characters avoids Unity crashing, however if you are working with VR it only supports Dx11, so then you'd have to switch

I think it is standard Unity error, yes. Аnd it's not related to СС4.