[rmcp-client] Preserve OAuth Auto-mode read failures

[stevenlee-oai]

Codex Thread 019edd6d-6f14-74e2-853c-345d1803d4a6

Superseded

This layer has been folded into #29017 so the first PR in the stack is independently correct.

#29017 now preserves an Auto-mode keyring reread error when no fallback credential exists and includes the regression test that ensures a storage failure cannot clear the live manager credential.

The active replacement stack is:

1. [rmcp-client] Serialize MCP OAuth refresh ownership #29017 — Serialize refresh transactions and preserve Auto read failures
2. [rmcp-client] Reread persisted OAuth credentials before refresh #29020 — Reread persisted credentials authoritatively
3. [rmcp-client] Serialize MCP OAuth login and logout #29019 — Serialize login/logout and bound waits
4. [rmcp-client] Serialize shared MCP OAuth stores #29021 — Serialize shared File/Secrets stores
5. [rmcp-client] Route all MCP OAuth recovery through Codex #29018 — Keep refresh ownership in Codex and recover once from 401