chat: delete sessions + auto-refresh the /chat list after each turn

DELETE /chat/sessions/:id removes Claude's transcript file; the list gets a
per-row delete button. The list also invalidates on turn-complete so new and
continued sessions surface without a manual refresh.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/servers/api/chat/chat.ts

@@ -1,5 +1,5 @@
 import { createRouter } from '../../create-router';
-import { getClaudeSessionsCwd, listClaudeSessions, loadClaudeSession } from './claude-sessions';
+import { getClaudeSessionsCwd, listClaudeSessions, loadClaudeSession, deleteClaudeSession } from './claude-sessions';
 
 export const chatRouter = createRouter();
 
@@ -18,3 +18,11 @@ chatRouter.get('/sessions/:id', (ctx) => {
   if (!detail) return ctx.text('Not found', 404);
   return ctx.json(detail);
 });
+
+// DELETE /chat/sessions/:id — remove a conversation (deletes Claude's transcript file).
+chatRouter.delete('/sessions/:id', (ctx) => {
+  const email = ctx.get('user').email;
+  const ok = deleteClaudeSession(email, getClaudeSessionsCwd(email), ctx.req.param('id'));
+  if (!ok) return ctx.text('Not found', 404);
+  return ctx.json({ ok: true });
+});