Adopt the ProblemDetail customizer, re-export the spec, republish clients

[ExtraToast]

What to build

auth-api adopts the shared error-response customizer, re-exports its committed spec, and republishes its clients — which now carry both the error schemas and the TanStack Query artifacts.

This is the first service to go through the full new pipeline, and its client is what the pilot UI consumes.

Acceptance criteria

• The committed spec declares error responses as application/problem+json for every operation
• The export drift gate passes, so the committed spec matches live springdoc output
• The breaking-change check reports the addition as non-breaking
• The republished client is verified by reading the published package — it exposes query options and the error schema

Blocked by

• Attach ProblemDetail error responses to every operation
• Emit TanStack Vue Query artifacts behind a subpath export
• Add a workflow_dispatch republish path for API clients