I was thinking maybe joules/year e.g. energy/time might be some brightness indicator for some astronomical definition of brightness - especially in the non-optical wavelengths.

But that's division, not multiplication. Another thread in my brain thought maybe the product of the two could be useful for people in that field, sort of how ISP is useful to people in rocketry but us normal people need to divide it by G(earth) to get something intuitive.