I personally hate status reporting because it is a means to an end and we often forget what the end is. Commonly it is something on the line of “I want you to report your status so that I can decide if I need to take action here or if I can ignore it”. Which I find you can achieve better if you skip the status reporting and just jump to the. Is there anything you need me to act on.
Then it is also not uncommon for you to be in the middle here and someone asks for status from you so you ask for status from your team etc. Again be more transparent and say something like I need to let my manager know if they need to act on anything, is there anything you want me to flag.
All of that being said my experience is that if you can show, through your actions, that if they need help you will help and if they do good they will get praise, people have a natural tendency to report to you anyway.
If being updated for instance is so you can take better decisions in unexpected meetings you will be called into. Apart from making that fact known a quick stand-up every morning is a good format. Again to reinforce the behavior praise is key. So for instance if one member said something in a meeting that you used, make sure to thank them for it and praise them. That way they can all get a better understanding of what kind of information you need and they can see the value of that. And on top of that they maybe get some information on what is going on etc.
We also share with each other bugs we have found (when they are of general interest) and tools we have started to use etc.