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

server/github/queries.ts

@@ -11,6 +11,7 @@ export const LIST_QUERY = /* GraphQL */ `
           title
           url
           isDraft
+          mergeable
           updatedAt
           author { login }
           headRefName
@@ -34,6 +35,7 @@ export interface ListPr {
   title: string;
   url: string;
   isDraft: boolean;
+  mergeable: 'MERGEABLE' | 'CONFLICTING' | 'UNKNOWN';
   updatedAt: string;
   author: { login: string } | null;
   headRefName: string;