Here are my thoughts -
I think Bullet behavior would be a poor choice for a billiards game, it's very inaccurate. Physics may work a little better as you can set "Collision mask=circle" for balls, but I'm still not sure.
If you want precision, you will need to calculate reflection angles and collision points in advance. Collision points too because a fast moving ball can travel long distances in one tick and if you rely on C2 collision detection, it will also be very inaccurate.
You can also try these plugins: