However, one unfortunate bit is that the board (in my case, the TV connected to the Switch) is "read-only" and you don't interact with it, unlike real life. You pick which card to play on your phone, and then place it onto the board also on your phone. So basically, all the action is on your phone, and the central board is kind of an afterthought. It doesn't feel as much like interacting with a shared space as I was hoping.
I'm not really sure how to solve that. I thought of some weird stuff (like, maybe after you pick your card, your phone is just a touchpad controlling the card as it now moves around on the big screen) but nothing seemed practical.