Mobile phone monitoring

You can install spyware. Its invisible software on his phone that connects to your phone.

But the issue is why you'd want to spy on your son? I feel like theres perhaps a better way to tackle behavior than spying.

Yes, it's plenty of them, look for "parental control" apps. The default ones are Family Link for android (you need to install this by the playstore, I use this one) and Family Sharing for apple (you can already find the parental control options in your apple account and in his one linked to your account). I strongly suggest you to start with one of these.

What do you mean with "alerts"? These parental controls above just set limits and restrictions for screen time, allowed apps and inappropriate stuff, you can see something of their web history but these don't alert you when he try to look for something inappropriate.
We tried several parental control apps, from what I've seen Bark is the only one that sends those kind of alerts but it requires a fee. Recently I found out Safe Lagoon that takes screenshots of anything used on their phones, so it's the most effective and complete monitoring, it requires a fee too (I purchased this and I think it's worth it if you need more control and a complete report of what they are doing on their phones).

What would be the best for you depends on your son's age, his inclinations and behavior, anyway I would start with the free standard one by android or apple and eventually if needed add a more complete one. The paid parental control apps have a free trial period of a week, you can test several ones to find what is the best for you.