The least expensive option with a zoomable camera may be to use an Atomos Connect (or similar capture device). You can use just about any camera. Even a handycam or regular digital camera if it has an HDMI out. It is thumb drive sized dongle that has a USB input on one side and an HDMI receptacle on the other.
The computer sees whatever video input plugged into the dongle as a webcam. So you can even use this to make higher end Zoom and other video conferencing calls. Plug your mic right into the camera for good in-sync audio.
Use OBS to stream anywhere with your laptop. There are a lot of different scoreboard apps that work with OBS. Just google 'OBS Scoreboard' or 'OBS Basketball Scoreboard'. There are lots of options. You can run a real deal game.
This works on the same principle as the Atomos Connect just much higher end with many more features --- If you already have a camera or cameras - look into the 'ATEM Mini Pro'. You can live stream and switch 4 different video sources plus throw up graphics and do picture -in-picture like you are ESPN. ($600).
https://www.atomos.com/connect-4k