Downloading the Bottle Tarfile

See here.

1. Fetch the manifest:

curl --location \
  -H'Accept: application/vnd.oci.image.index.v1+json' \
  -H'Authorization: Bearer QQ==' \
  https://ghcr.io/v2/macaulay2/tap/macaulay2/manifests/1.23

2. Use jq to parse the json output, for instance to get a bottle digest:

curl ... | jq '.manifests[0].annotations."sh.brew.bottle.digest"'

3. Download the bottle

curl --location --request GET -H'Authorization: Bearer QQ==' \
  https://ghcr.io/v2/macaulay2/tap/macaulay2/blobs/sha256:[digest] --output macaulay2-1.23.tar.gz

Alternatively, you can get the location from:

curl --head --request GET -H'Authorization: Bearer QQ==' \
  https://ghcr.io/v2/macaulay2/tap/macaulay2/blobs/sha256:[digest]

and download the bottle using wget.