I have a similar problem, perhaps this is a duplicate but I didn't find any other discussions around this problem.
I've successfully installed the Paclet but found it hard to get off the starting block:
Needs["ChristopherWolfram`OpenAILink`"]
PacletSymbol["ChristopherWolfram/OpenAILink",
"ChristopherWolfram`OpenAILink`$OpenAIKey"] = "<myAPIKey>";
Set::write: Tag PacletSymbol in PacletSymbol[ChristopherWolfram/OpenAILink,ChristopherWolfram`OpenAILink`$OpenAIKey] is Protected.
that error message may be hard to see but is says the Tag is Protected. $OpenAIKey = "<myAPIKey>";
However, I was able to get around the issue by directly evaluating the above code.