The following documentation suggests that it's possible to fetch public SSH keys using OAuth (see the "Account" section):
https://developer.atlassian.com/bitbucket/api/2/reference/meta/authentication

This does not reflect the truth, however - When attempting to fetch the SSH keys using OAuth, the following response is thrown:

#!bash
{"type": "error", "error": {"message": "This API is only accessible with the following authentication types: session, password, apppassword"}}