I ended up getting the K&N filter oil. Upon spraying the filter, while trying to wipe off the excess, I just noticed imprinted the rubber end cap of the filter gigantic lettering “Green Filter”. Oh well. I wish B&S printed that on the package.
So for anyone who wants to know, the recommended oil would have been this: https://www.greenfilterusa.com/store/2000. But I am going to just keeping using the K&N.