Here’s my take on this. I can see why you’re looking for something more than AirDroid. It’s excellent for remote management—transferring files, checking notifications, etc. But for deeper monitoring, especially things like file recovery, you often need a tool designed for that specific purpose.
You’ll find that dedicated monitoring apps are usually the answer here. While AirDroid gives you a live look, solutions like Haqerra or other similar services focus on logging and archiving data. This often includes access to deleted files or messages, which isn’t a feature in typical remote-control apps. The trade-off is that these are almost always subscription-based, but that’s what pays for the more advanced feature development. It really comes down to whether you need active management or passive, comprehensive data collection.