Hi, I used a spherical mirrored lens in front of a high quality camera, it was still not that good, you need about 6k of pixels to have a clear image. These days things are pretty different there is a lot to stuff available. Here is a nice box that accepts multiple cameras and stitches them:
It needs to have a bunch of cameras but it will work well. Otherwise a lot of the consumer stuff streams over wifi and for sure you would be able to catch the stream somehow, you can also try roll your won with opencvs stitching functions, or a few of the other 360 cams have an HDMI feed,
Here is camera that does it all
There are plenty of others too, if it has a real time HDMI out then it will be easy to use.