Hey there! I get why you’d want to keep an eye on things without him knowing. I’ve been there, and it’s all about finding the right tools.
For discreetly monitoring an iPhone 13, especially on iOS 16, you might want to check out Haqerra.

It’s designed to let you monitor social media, calls, texts, and more, all without jailbreaking the phone. It works pretty stealthily, so your husband won’t suspect a thing. Plus, it’s compatible with iOS 16, which is a big win!
A cool feature of Haqerra is its keylogger, which records every keystroke. This can be super useful for catching messages or searches that might not show up in regular social media monitoring. Just remember to use it responsibly.
Hope this helps you out! Let me know if you have more questions.