Yeah totally normal concern, and honestly the good news is Apple’s built-in stuff is pretty solid before you go downloading anything third-party. If her iPhone is on your Apple ID family plan, Screen Time (Settings > Screen Time > Family Sharing) lets you see app usage and set limits without touching her phone beyond the initial setup.
For actual message monitoring, most legit apps like Bark or Qustodio do require physical access once to install, but Bark is probably the most “privacy-respecting” option since it flags concerning content rather than just dumping every text to you - which honestly is a better approach with a 13-year-old anyway. The completely “no-touch” remote solutions you see advertised are usually either scams or require jailbreaking, neither of which you want.