Where does a photon('s energy) originating from the sun's core spend most of its time?

AFAIK the photons inside a star essentially perform a random walk until they leave. Considering these factors:

• closer to the core the curvature of the sphere that seperates "closer to the core" from "further from the core" is higher, so initially a step in the random walk will be more likely to increase the distance from the core than later on, where I am assuming the seperating surface locally get flatter and flatter, and such the probability of "random walk gets closer to core" and "random walk gets closer to star surface" will get increasingly equal.

• density closer to the core is higher, so a step in the random walk towards the core will statistically be a little shorter until the photon gets reabsorbed than if the step is towards the surface.

Taking these two together I would guess that there is, or could be, a shell from r1 to 2*r1 (probably somewhere near the core) where photons from the core stay longer during their random walk than in the radius r1. Since the volume grows cubically with distance, it’s probably not hotter in that volume than inside r1.

Is r1 > 0 and if yes, what is it? And does it have any physical implications?