A VPN stands for a Virtual Private Network. So by being logged in on your phone that is creating one virtual private Network and when you log in through your box that's another virtual private Network. So in essence your phone is on a different Wi-Fi than your box. I have found some vpns that still work oh, I believe when I used either nordvpn or TunnelBear I can't remember I was able to still cast. But other vpns depending on how they set up on their end won't be compatible for casting and control. If your router has the ability to implement v p n then your best bet would be to do that unfortunately a very limited amount of routers and mostly Asus routers allow that out of the box. If you're technically savvy you can flash your router or modem would something like this

https://vpnoverview.com/vpn-setup/install-vpn-router/

If you have an old router or an old modem line around I would probably practice with that first so you don't brick your router if you're not familiar with this type of technical know how

If you have an old raspberry pi you can also do this project

https://www.google.com/amp/s/thepi.io/how-to-use-your-raspberry-pi-as-a-vpn-router/amp/

This way you don't need to install and turn on the VPN on all your individual devices but will still have the security of v p n straight from your router oh, this should allow you to cast and have the ability of all your network access that you're used to

which android box are you using?