cursor-cli: wire session resume with chat ID persistence

[mafredri]

Problem

Cursor CLI supports cursor-agent --resume [chatId] and agent resume, but the module always starts fresh. Unlike the other agents, resume requires a chat ID from the prior session, and the module has no mechanism to capture or persist one.

--type cursor is already present. No --type change needed.

Desired outcome

• On cold start: Cursor starts normally. The chat ID from the new session is captured and persisted.
• On warm start: Cursor resumes the prior session using the stored chat ID. The task prompt (currently a positional arg) is not re-sent.
• After feat(coder/modules/agentapi): add state persistence #736 lands: enable_state_persistence = true.

Investigation needed first

The exact mechanism for capturing chat IDs is undocumented. Before implementation, test:

1. Parse cursor-agent ls output for the most recent chat ID.
2. Monitor ~/.cursor/chats/ for new entries after launch.
3. Capture from process stdout.

Also verify:

• What happens when --resume <chatId> is called with an invalid or missing ID?
• Does --resume work in non-interactive/headless mode (as launched by agentapi)?
• The format of ~/.cursor/chats/ is undocumented and may change without notice.

If no reliable capture mechanism exists, this ticket is blocked.

Version bump

minor