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

web/src/components/PrCard.tsx

@@ -38,6 +38,7 @@ export default function PrCard({
       </div>
       <div className="meta-row">
         {pr.isDraft && <span className="draft-tag">draft</span>}
+        {pr.mergeable === 'CONFLICTING' && <span className="conflict-tag">⚠ conflicts</span>}
         <span>{pr.author}</span>
         <span className="branch" title={pr.branch}>
           {pr.branch}

web/src/styles/app.css

@@ -308,6 +308,16 @@ button {
   color: var(--ink-secondary);
 }
 
+.conflict-tag {
+  border: 1px solid var(--status-fail);
+  border-radius: 4px;
+  padding: 0 5px;
+  font-size: 11px;
+  font-weight: 600;
+  color: var(--status-fail-text);
+  background: var(--chip-fail-bg);
+}
+
 .branch {
   font-family: ui-monospace, monospace;
   font-size: 11px;