Yes, you can play Diablo 4 solo, and you don’t need a subscription for the game. It’s a one time purchase. The main map is connected online and is the same map for everyone. You can see other players occasionally, depending on your region server. It’s kind of like Destiny 2 that way.
I primarily play games on PC. I have a Switch that I use every once in a while, and I recently bought a Retroid pocket 3+ for emulating games on a handheld.