helm harbor is not a valid chart repository or cannot be reached: object required

Question

I've successfully pushed some locally built helm chart to harbor private helm registry using below commands:

helm registry login private.harbor.com
helm push chart-version.tgz oci://private.harbor.com/some-project

Now I fail to add helm repo (for the goal of installation of the pushed helm chart) using below commands:

$ helm repo add helm-test2 oci://private.harbor.com/some-project/
Error: looks like "oci://private.harbor.com/some-project/" is not a valid chart repository or cannot be reached: object required
$ helm repo add helm-test2 oci://private.harbor.com/some-project/helm-test-repo
Error: looks like "oci://private.harbor.com/some-project/helm-test-repo" is not a valid chart repository or cannot be reached: object required
$ helm repo add helm-test2 https://private.harbor.com/some-project/helm-test-repo
Error: looks like "https://private.harbor.com/some-project/helm-test-repo" is not a valid chart repository or cannot be reached: error unmarshaling JSON: while decoding JSON: json: cannot unmarshal string into Go value of type repo.IndexFile
$ helm repo add helm-test2 https://private.harbor.com/some-project
Error: looks like "https://private.harbor.com/some-project" is not a valid chart repository or cannot be reached: error unmarshaling JSON: while decoding JSON: json: cannot unmarshal string into Go value of type repo.IndexFile

How to helm repo add Harbor OCI helm repository?

It's important to note that docker images are stored alongside pushed helm charts at private.harbor.com/some-project/.

Alternative way that worked is uploading helm chart under Helm charts tab in some-project in Harbor UI.

Afterwards, below commands for adding and installing the chart worked:

helm repo add helm-test https://private.harbor.com/chartrepo/some-project
helm repo update helm-test
helm install chart helm-test/chart --version 1.5.0

I would use this method, but have no idea how to push to https://private.harbor.com/chartrepo/some-project, pushing to oci://... worked only after following this github link.

Below attempts failed:

helm push chart-version.tgz oci://private.harbor.com/chartrepo/some-project
Error: unexpected status: 401 Unauthorized
helm push chart-version.tgz https://private.harbor.com/chartrepo/some-project
Error: scheme "https" not supported

I'm using latest helm (3.8) and harbor version (2.5)