And it takes about a million years for that energy to travel to the surface of the Sun and escape. The total output of the Sun is 4e26 watts. Multiply by 3e7 seconds in a year and 1,000,000 years and get 1.2e40 joules. Divide by the speed of light squared and get 1.3e23 kilograms. The Sun weighs 2e30 kg thus the trapped photons account for about one millionth of one percent of the Sun's mass.
It's also gotten brighter, which I guess I would too if I could lose that much weight.
The Random Walk seems to have a host of random time value estimates. There was one paper that gave something like 18,000 years, but it made density a constant instead of a variable. So, a million years is likely a closer number.
But light reaches the upper photosphere, perhaps about 200 km from the "surface", then it finally launches into space.
Getting back to a week ago... I assume, once again, this is because of the amount of molecular hydrogen granting passage. Is this likely?
Also, notice that the Sun does have something close to a blackbody profile even though it is comprised of mainly hydrogen. So this also may help us see how we can still get a blackbody from a single element (mostly), though highly thermalized, I suppose.