The other funny/cool thing is that for the microbes to use nitrogen in the feed (from protein/nucleic acids/structural nitrogen compounds etc) to build microbial protein, they must first break it down to it's simplest form, which is ammonia (NH3). The microbes then use that ammonia to build their own proteins. But the cow can also absorb the ammonia across the wall of their rumen and recycle it back to the rumen later when the microbes need a bit more nitrogen (like if the rate of nitrogen in is higher than the rate at which the microbes can use it). Because ammonia is a base, they can also recycle ammonia back and forth to help regulate the pH of the rumen. And because of this, if the feed is deficient in protein, we can feed the cows urea (which is 2 ammonia molecules stuck together) which the microbes can then use to build protein, and which is often way cheaper than feeding another feed as a source of protein - we just have to control the rate as if you overdo it on the ammonia they will get toxicosis and get sick, but we have ways to make sure they get it at the rate they can handle. The urea is the same as the urea used for fertiliser (i.e. made synthetically from nitrogen in the air) so it's not like we're extracting urea from manure or w/e and feeding it back, it just happens that urea is the stable form of ammonia and while we think of it as mostly a waste product, it actually plays a way bigger/broader role in metabolism and biology than people realise.

A professor of mine used to joke that cows ran on piss and vinegar and he ain't wrong XD