You asked the question, it's only fair that you do the counting. Memory Alpha has a list of species to get you started.
Most of each of the series is dominated by humanoid species simply due to the economics of it or due to the progenitors in story. But, I seem to remember just as many, if not more non-humanoid species newly introduced in TNG in addition to the ones that first appeared in TOS.
"Darmok" was the only other episode Robin Lefler appeared in The Next Generation.
Watching LLMs try to interpret context is like that episode of Futurama where Bender tries to be a chef.