Hi Stephanie!
We generally recommend going through the admin API, as in most cases businesses need to do extra checks and delete more data, so having your own delete endpoint gives you maximum flexibility.
As for admin credentials - we will introduce more flexible API keys with limited permissions in the coming months, so from our perspective you can go with the Admin API approach and later reduce access for the calling service.
A client-side delete - once we build it, there's no definite estimate for that right now - would come with a webhook to react on the event and perform additional steps. However, we also appreciate that some clients would rather do a soft-delete (wiping PII, removing credentials, locking the account) with subsequent hard delete after some time, so we have yet to decide what a good out-of-the-box solution looks like.
Your solution with oathkeeper to send DELETE requests to a separate service that orchestrates the Ory deletion with other actions in your system does sound like a good approach to me!