What is the true physics of plane rotation?

I've learnt that when a body undergoes circular motion it need a force perpendicular to the bodies velocity and towards the centre of the circle for the body to stay in circular motion. However when I try to find if planes have this force towards the centre of earth (that I assumed would be a non-zero resultant force of gravity/weight and the lift force) I keep finding that the resultant force is zero, which I don't understand.

I think either:

My understanding of circular motion is to basic/wrong, or

the people online are using linear and not rotational mechanics, or

the force is so small most people say its negligible and so basically zero.

Can someone please tell me which one of these is right if any.

(You don't have to but an explanation if I'm wrong would be nice)

Thanks for taking the time to read anyway!