Download repository as zip using repository access token

I want to switch from using app passwords to repository specific access tokens. However, I could not find a Bitbucket API which supports this.

The following fails:

curl --request GET --url 'https://bitbucket.org/<user>/<repository>/get/master.zip' --header 'Authorization: Bearer <access token>'

{“type”: “error”, “error”: {“message”: “Token is invalid or not supported for this endpoint.”}}

I guess this endpoint does not support access tokens. Is there another API to do the same or will this be supported in future? Using app passwords is not granular enough and access tokens would be the ideal use case. I hope there is a way to use this.

Thanks,
Christoph