exile.watch packages utilize the GitHub NPM registry.
Working with the GitHub NPM registry requires tokens with read permission. Therefore, a PAT is needed, even if you only wish to access public repositories (a.k.a. public packages)
Instructions for generating a GitHub PAT (Personal Access Token) can be found here.
Apart from naming your token, no additional modifications are necessary on your part.
Ensure that Repository access includes Public Repositories (read-only) checked.