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;

server/poller.ts

@@ -37,6 +37,7 @@ function signature(pr: ListPr): string {
         pr.reviews.totalCount,
         pr.latestReviews.nodes.map((r) => `${r.author?.login}:${r.state}`),
         pr.labels.nodes.map((l) => l.name).sort(),
+        pr.mergeable,
       ]),
     )
     .digest('hex');
@@ -82,6 +83,7 @@ function buildSnapshot(config: AppConfig, pr: ListPr, detail: DetailPr | undefin
     url: pr.url,
     author: pr.author?.login ?? 'ghost',
     isDraft: pr.isDraft,
+    mergeable: pr.mergeable,
     branch: pr.headRefName,
     updatedAt: pr.updatedAt,
     labels,