https://en.wikipedia.org/wiki/Whey_protein#Microbial_product...
It's not theoretical either. You can buy vegan dairy products made from this method today.
In addition, you'll need more cleaning/sterilization/mixing. I'd guess that it's lower, but I wonder how much lower.
And then there's the other products that generally get thrown into the mix to make up for things like missing fats. For example, a vegan cheese based on bacteria will often include coconut oil, probably to get the same fat profile.
Whey is an interesting product in general because it's a waste product of cheese making.
Feed efficiency is critical when doing these calculations as cows inherently need energy to survive not just produce milk. As such even if you use the same crop two different sources of protein can have wildly different levels of CO2 emissions embedded in their creation. https://en.wikipedia.org/wiki/Feed_conversion_ratio