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/claude-sessions.ts

@@ -1,4 +1,4 @@
-import { readdirSync, readFileSync, existsSync, statSync, mkdirSync } from 'node:fs';
+import { readdirSync, readFileSync, existsSync, statSync, mkdirSync, rmSync } from 'node:fs';
 import { join } from 'node:path';
 import { DATA_PATH } from '../../data-path';
 
@@ -187,6 +187,14 @@ export function loadClaudeSession(email: string, cwd: string, sessionId: string)
   return { id: sessionId, model, cwd: sessionCwd, messages };
 }
 
+/** Delete a session by removing its transcript file. Returns false if it didn't exist. */
+export function deleteClaudeSession(email: string, cwd: string, sessionId: string): boolean {
+  const filePath = join(claudeProjectsDir(email), projectSlug(cwd), `${sessionId}.jsonl`);
+  if (!existsSync(filePath)) return false;
+  rmSync(filePath);
+  return true;
+}
+
 /** List sessions Claude has stored for a given working directory, newest first. */
 export function listClaudeSessions(email: string, cwd: string): ClaudeSessionSummary[] {
   const dir = join(claudeProjectsDir(email), projectSlug(cwd));