Your assumption regarding splitting known species is wrong as it comes to numbers. It often happens for birds but this doesn't move the needle as there's only 10K birds.
Almost every species on this planet is an arthropod and most are not described. It's trivially easy to "discover" new ones. Go to a bio-diverse area (say a jungle) and fill a wheelbarrow with soil. Filter the dirt and describe anything you find. It will take you forever but there will be dozens if not hundreds of "new" species. The main bottleneck is not finding them, it's describing them, which is very time consuming.
Put some specialized lights up in the same area at night. One remote site I attended in Colombia discovered on average 20 new species of moth every single day. There's expected to be 150K moth species, which still may be an underestimation.
And this doesn't even describe the truly tiny organisms living in soil and rivers and oceans.
As it comes to species, the public has a bias for mammals and birds. Combined they're about 17-18K species only. Not even a drop in the ocean. You can split each of them into 10 separate species and this still doesn't do anything to inflate the total amount of species.