Yet, the minimum optical power source range that this photodiode is recommended to be used at is 1nW/cm^2 which is way, way below the 10uW/cm^2 that was being used in the estimate above.
Note that the photodiode is advertised for use in photovoltaic mode, but the dark current is speced with a reverse bias (so in photoconductive mode where dark current is a bigger problem). For very low light they expect you to use photovoltaic mode.
Because there is a version of this photodiode with much smaller area and the dark current is lower but so too is photocurrent and they just pretty much scale with each other. If so, what's the point of choosing a larger sensor (for applications where you're not blasting a laser at it)?
This is a great optical engineering question. The maximum radiance of a photodiode goes up with the active area, but the number you are looking at (10uW/cm^2) has units irradiance, which does not have the same relationship. The difference is that radiance cannot be increased by optics (or anything), but irradiance can be using a simple lens. If you really care about irradiance, then you would get a lens and use it to focus down onto a tiny photodiode. Since dark current scales with area, this would allow you to divide your dark current by a factor of hundreds or thousands at no loss of irradiance. The smaller diode would also be cheaper, faster and introduce less electronic noise into your opamp.
The reason larger photodiodes exist is due to radiance. A lens trades (via the Fourier transform) angle for position, so focusing only works if the source has a narrow range of angles (which you can Fourier transform into a narrow range of positions). Try to focus sunlight on a sunny day works well. Try it on a cloudy day (when the light comes from clouds at all angles) and the lens does nothing. In your case, if your source of UVA comes from a single, compact source (like an LED) and that source is stationary, you can point a 2 cm lens at it with a 100 micron photodiode and get the same photocurrent as using a 2 cm detector. This will make your dark current insignificant.