Stop publishing to heroku/heroku-private on Docker Hub (#246)

The base images are currently double-published to Docker Hub - once to
the public `heroku/heroku` repository, and then again to the private
`heroku/heroku-private` repo.

Publishing to `heroku/heroku-private` was added in:
#130

...with the explanation that it might help internally with rollback use-cases.

However:
1. We've never had cause to use this private repository for rollback in
   the 5 years since.
2. We now have a robust image rollout and rollback process, which doesn't use
   these images, but instead Cheverny (for the S3 image releases) and image
   tags on the `heroku/heroku` repo for the Docker image side:
   https://github.com/heroku/cheverny/blob/main/docs/base-image-release.md#rollback-process
3. The author of the PR that added the publishing of these images has
   confirmed that there isn't some other reason for keeping them:
   https://salesforce-internal.slack.com/archives/C01068P24S3/p1707346168976339

As such, we can stop publishing to this repository to simplify the
publishing process (which is going to be getting a lot more complex
for multi-arch support soon).

GUS-W-15018626.

bin/publish-to-registries.sh

@@ -29,25 +29,20 @@ push_group() {
     done
 }
 
-date=$(date -u '+%Y-%m-%d-%H.%M.%S')
 publicTag="heroku/heroku:${STACK_VERSION}"
-privateTag="heroku/heroku-private:${STACK_VERSION}"
 internalTag="${INTERNAL_REGISTRY_HOST}/s/${ID_SERVICE_USERNAME}/heroku:${STACK_VERSION}"
 
-# Push nightly tags to dockerhub (e.g. heroku/heroku:22.nightly)
+# Push nightly tags to Docker Hub (e.g. heroku/heroku:22.nightly)
 push_group "${publicTag}" ".nightly"
 
-# Push date tags to private dockerhub (e.g. heroku/heroku-private:22.2022-06-01-17.00.00)
-push_group "${privateTag}" ".${date}"
-
 if [ "$GITHUB_REF_TYPE" == 'tag' ]; then
-  # Push release tags to dockerhub (e.g. heroku/heroku:22.v99)
+  # Push release tags to Docker Hub (e.g. heroku/heroku:22.v99)
   push_group "${publicTag}" ".${GITHUB_REF_NAME}"
 
   # Push release tags to internal registry
   push_group "${internalTag}" ".${GITHUB_REF_NAME}"
 
-  # Push latest/no-suffix tags to dockerhub (e.g. heroku/heroku:22)
+  # Push latest/no-suffix tags to Docker Hub (e.g. heroku/heroku:22)
   push_group "${publicTag}" ""
 
   # Push latest/no-suffix tags to internal registry