Show merge-conflict badge on PR cards via GraphQL mergeable field

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DgBEW6qAwgn2fcQbA2f4ZQ

shared/types.ts

@@ -34,6 +34,8 @@ export interface PrSnapshot {
   url: string;
   author: string;
   isDraft: boolean;
+  /** GitHub's merge-conflict state; UNKNOWN while GitHub is still computing it. */
+  mergeable: 'MERGEABLE' | 'CONFLICTING' | 'UNKNOWN';
   branch: string;
   updatedAt: string;
   labels: string[];