As far as I understand, photons are massless, but are still subject to gravity, must follow the distortions of spacetime (including framedragging etc.), period.

Now the only answer on this site explains the disk shape of the accretion disk with the conservation of angular momentum. But, as far as I understand, photons are subject to this law too, and should be framedragged by the black hole, and following this line of argument, should be ordered into a disk shape or "photon disk".

Now photon spheres are not always spherical, there are different forms, depending on the conditions of the black hole (rotation etc.), but they can hardly be disk shaped.

reason the orbits lie roughly in the same plane: Conservation of angular momentum.

Why do all the planets of the solar system orbit in roughly the same 2D plane?

Because the total angular momentum is conserved, this angular momentum lost by the object that is getting closer must be transported to the rest of the disk that gains the angular momentum. This tends to flatten the disk and align the direction of rotation of all the parts because flattened uniformly rotating disks maximize the angular momentum vs energy ratio. And that's what the dynamics prefers because the kinetic energy is being lost (converted to heat etc.) while the total angular momentum is being increased.

Accretion disk physics - Stellar formation

At this point, one could say, that photons cannot slow down, they cannot transfer their angular momenta. But, photons can and sometimes do transfer their momenta to other objects (solar sail, radiation pressure, mirror etc.), in this case they could transfer their momenta to the black hole's gravitational field itself, thereby "flattening" the photon sphere. And, photons are subject to frame dragging (they must follow the distortions of spacetime), based on the rotation of the black hole.

So there are a few things that come to mind:

1. the accretion disk gets its shape from angular momentum conservation

2. angular momentum conservation holds for photons too

In other words, why is the photon sphere not disk shaped, because of angular momentum conservation, just like an accretion disk? Again, why does this mechanism not "flatten" the photon sphere?

Question:

1. Why is the photon sphere spherical, but the accretion disk not?