Three things happened at once last night: Raiders attacked Sanctuary Hills, the population went to 11, and a Brahmin showed up. The Brahmin does not count as my 11th settler, there is an actual settler for that, but where did this Brahmin come from? Is it a consequence of having more than 10 settlers?
The Brahmin come with settlers. They use them to carry their things from wherever they came from to your settlement. If you set up a supply line, they will walk around with Brahmin a lot, as a symbol that the supplies on the Brahmin are carrying things back and forth.
No this isn't because you have more than 10 people.
And no clean up is required, they don't poop.
Edit: If it's a Brahmin that isn't carrying anything, then it's a wild one. You can find them out in the world sometimes in a pack. Sometimes they can wander into your settlement if it's too open or if another animal chased it that way.
The wild ones don't poop either.
The Nukapedia page on Brahmin indicates that they will sometimes be recruited by your recruitment beacon instead of a settler:
When actively recruiting for a settlement with a recruitment radio beacon, there is a chance to receive a brahmin instead of a settler.
That seems consistent with my in-game experience, in that Brahmin usually show up in settlements that have a few people, which are settlements where I've set up beacons. But, if someone has a Brahmin in a settlement that never had a beacon, it would act as a counterexample.
It also indicates that the Brahmin produce fertilizer in your workshop, and that they increase food production:
Brahmin will increase settlement food production while also producing fertilizer, a component for chemistry that will be placed in the workbench.
I've seen no in-game evidence that that's true. I'm willing to believe that they produce fertilizer, but I'm highly skeptical of the food production claim. I've always been able to account for 100% of my food production via crops, with no extra mystery component that could be attributed to the Brahmin. Perhaps they accelerate the collection of the actual crops, or the rate at which they regenerate after being harvested.
So, they're your Brahmin, and your settlers will clean up after them.
Occasional it seems a new settler will come with a Brahmin included. I have them on several settlements, some more than others. Did not figure out yet if you can move that same settler around and the Brahmin will follow. In that case you could move all your Brahmins to a single settlement and have your production of fertilizer (they do that) in one place. And you can make drugs from fertilizer and get rich! Or high....