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the token is still widely scoped and has the same scope as the PEMWhat the person above you is trying to tell is you is that no, it doesn't.
The authentication flow is that the private key is used to sign an initial JWT; that gets you access to some GH API calls. From there you exchange that JWT for an access token with smaller scope, scoped only to the installation in question.
While the tool execution environment ought to have had none of the credentials, there is the possibility of only holding onto the installation access token.