Friction between road and tyre resisting centripetal force. Newton’s equal and opposite reaction.
The angle is determined by how much friction is available. That depends on the road surface, what the tyre is made of, and how much of it is in contact with the road. I guess a racing tyre will be made of a soft rubber rounded to squidge more as the bike tilts. Better grip than a road tyre in exchange for rapid wear.
Obviously limits to how far a bike can tilt, and motor cyclists are extremely vulnerable to oil, water, ice, leaves, gravel, metal covers, or smooth asphalt repairs. Or expecting a road tyre to allow Guy Martin style cornering on the way back from the pub.
I’ve avoided the maths because I will certainly get it wrong. Look up centripetal force, or perhaps someone good at sums will explain!
Dave