I'm not familiar with Cursor, does it allow the agent to have access to run "curl -X POST" with no approval, i.e. a popup will show up asking you to approve/deny/always approve? AFAIK with Claude Code, this can only happen if you use something like "--dangerously-skip-permissions". I have never used this, I manually approve all commands my agent runs. Pretty insane that people are giving agents to do whatever it wants and trusting the guardrails will work 100% of the time.
Cursor's like Claude Code in this regard by default when executing external commands. But IIRC you can also click something like "Always Allow" and it'll stop asking.