A couple of those rows aren’t plugins Cursor installed - claude-mem (and likely one of the two Cloudflare entries) come from Claude Code. Cursor can’t remove those individually, so their trash icon opens Cursor Settings → Agents instead of deleting.
To remove them: uninstall in Claude Code, or turn off Include Third-Party Plugins, Skills, and Other Configs in Cursor Settings → Agents, then fully restart Cursor. Deleting them only inside Cursor won’t stick — they get re-read on startup.
For rules: your own rules delete from the “…” menu on the rule’s row in Customize → Rules. Plugin rules go away when you uninstall the plugin; Claude rules like CLAUDE.md are files on disk.
If a row still won’t clear after that, tell me which one you clicked and whether anything happened (nothing, or a Settings page opened) and I’ll dig in.