Add a setting to keep Agent terminals alive when switching chats

Describe the request

This makes Agent-driven local full-stack workflows fragile: frontends lose watch/recompile sessions; backends drop mid-debug. Users then must restart services one-by-one again.
Forum staff have described this as terminal rebind failure + intentional GC, not always an intentional product preference — but from a user perspective we need an opt-in keep-alive.

Why a setting matters

  • Some users want aggressive cleanup (current behavior).
  • Many local-dev users want Agent terminals to behave like normal Editor terminals: survive chat switches.
  • Without a setting, Agents cannot reliably “start services and leave them running” across sessions.

Proposed behavior

When keep-alive is enabled:

  • Switching Agent chats must not terminate the underlying process.
  • Terminals should remain listed and re-bindable (Terminal list / other agents group is fine).
  • Optional: only GC terminals after explicit user Stop, or when the workspace folder is closed.

Environment / context

  • OS: Windows 11
  • Use case: sequential start of multiple FE/BE services via Agent shells; frequent chat switches while coding
  • Current workaround: run services in classic Editor user terminals / Tasks (less convenient when asking Agent to start them)

Acceptance criteria

  1. A documented setting exists in Cursor Settings.
  2. With the setting ON, Agent-started long-running processes survive chat/workspace switches for at least N hours (or until user stops them).
  3. With the setting OFF, current GC behavior remains.
    Thanks — this would materially improve Agent-assisted local development.

中文摘要(方便你对照)

希望 Cursor 增加设置项:切换 Agent 会话/工作区时,可选择不关闭 Agent 拉起的终端及其中的长驻进程(如 ng serve / spring-boot:run)。
现状约 1 分钟重连宽限期后会杀进程,且没有开关;导致本地起服工作流不稳定。