fix(auth): bidirectional mode/type compat + sync OAuth to all agents (#12692)

Merged via /review-pr -> /prepare-pr -> /merge-pr.

Prepared head SHA: 2dee8e1174
Co-authored-by: mudrii <220262+mudrii@users.noreply.github.com>
Co-authored-by: obviyus <22031114+obviyus@users.noreply.github.com>
Reviewed-by: @obviyus

src/agents/failover-error.ts

@@ -51,6 +51,8 @@ export function resolveFailoverStatus(reason: FailoverReason): number | undefine
       return 408;
     case "format":
       return 400;
+    case "model_not_found":
+      return 404;
     default:
       return undefined;
   }