What is the photon interception radius of a Schwarzschild black hole? [duplicate]

To clarify what i mean by "photon interception radius" I mean the radius of the sphere where if any photons from a distant source enter will also inevitably result in them entering the black hole.

The photon interception radius must be at least the Schwarzschild radius since even without gravity a photon would still cross the event horizon.

It must also be greater than the photon sphere as while light can orbit there there is no way to exit or enter, any orbiting light must have been emitted sideways by matter on the way through. Any incoming light must come from further out and with a steeper angle.

My main question is at what radius a passing photon must be from a Schwarzschild black hole to avoid being pulled in and crossing the event horizon?

My secondary questions are how much orbiting/curving a borderline captured photon would undergo before crossing the horizon as well as how much orbiting/curving an infinitesimally further out escaping borderline photon would undergo before escaping into asymptotically flat space. (I imagine one of these would result in an arbitrarily close to infinite number of orbits meaning the point/angle at which it crosses the event horizon/escapes into infinity is undefined but I might be wrong. And while I drew the borderline photon crossing the event horizon at 180°/half an orbit worth or rotation I have no idea what it actually is, I just picked 180 because proper spiraling would be hard to draw.)

The term you are looking for is "critical impact parameter". As explained in this answer: https://physics.stackexchange.com/q/558665, the critical value of $$X$$ is $$3\sqrt{3}$$.