Cannot promote member from follower when auth is enabled

Bug report criteria

• This bug report is not security related, security issues should be disclosed privately via security@etcd.io.
• This is not a support request or question, support requests or questions should be raised in the etcd discussion forums.
• You have read the etcd bug reporting guidelines.
• Existing open issues along with etcd frequently asked questions have been checked and this is not a duplicate.

What happened?

In a cluster with auth enabled, member promotion operations fail and timeout if they are submitted to a follower member. The leader member repeatedly logs this warning:

failed to promote a member

Along with the error:

auth: user name is empty

What did you expect to happen?

The follower should forward the promotion request to the leader, and that promotion request should succeed.

How can we reproduce it (as minimally and precisely as possible)?

• Create a cluster with two members and enable auth
• Determine which member is the follower
• Add a learner member to the cluster
• Submit a "member promote" request to the follower member

I've written an E2E test that demonstrates this process here: https://github.com/jason-lynch/etcd/commit/58e8806987937d0200786e6c3f8ad797d60a14f6

Anything else we need to know?

No response

Etcd version (please run commands below)

I'm embedding Etcd in my project, and I'm currently at version 3.6.1. I've used my E2E test above to verify this issue on v3.6.1, v3.6.5, and the current head of main.

Etcd configuration (command line flags or environment variables)

No response

Etcd debug information (please run commands below, feel free to obfuscate the IP address or FQDN in the output)

No response

Relevant log output

failed to promote a member error="auth: user name is empty"