apparently JWST has already photographed Earendel; sciencealert.com/… but I didn't see any information about JWST taking a spectrograph of the star.

So for our universe, ignoring any differences due to the local speed of the Earth and Sun's velocities. and the velocity of the distant galaxy then the maximum angular diameter distance occurs where the expansion of the universe is equal to the speed of light when the light from the distant galaxy was emitted, correct?

@pela fee; free to elaborate. Perhaps there is something special about the speed of the expansion of the universe relative to the Earth at the time the light from a $z\approx 1.62$ galaxy was emitted that makes the curve turnover and peak at around 5.80 billion light years angular distance. Is it possible that when the light was emitted, the relative velocity of the galaxy was equal to the speed of light???

@ProfRob Are there any type 1a supernova candidates that are very close to the Chandrasekhar Limit of 1.4 solar masses? I could post a separate question ...

There are $5\cdot 10^{40} m^2$ on the surface of a sphere radius 6700 light years, so the expected wattage per m^2 would be significantly lower than the sun. 9.4*10^15 meters/light year.

Its an extremely good approximation! For $\theta$ converted to radius, where $\theta=1"\cdot\frac{\pi}{180\cdot 3600}$ then $\frac{1}{\tan(\theta)}\approx\frac{1}{\theta}$ is accurate to better than 1 part in 10^10.