for month I have been struggling with the same issue.
I have found this post from Reddit but it doesn't seem to work.
I have tried then using the Google's API explorer and the correct type appears to be cvt_galleryTemplateId

I also tried cvt_containerId_templateId as suggested on Reddit but had no luck (but in the past I was able to, using Python).
I am not sure then what's the correct type as Google's documentation is crap.

I am writing a function to autoamte the copy between container to create a MCP server so I hope I will solve this.

I'd suggest to do some tests using the API Explorer to better understand how it works.

Good luck