47 third party, 20 first party. However, some of those are hard to pin down like Dragon Quest 11 and Octopath Traveler. Nintendo published them and is listed as the publisher on the games overview screen on the Switch, so what are they? To me those are Square Enix games. The same applies for Snipperclips, Marvel Ultimate Alliance 3, Astral Chain and Daemon X Machina. And where does Mario x Rabbids belong to?
However, the majority is third party anyway.
There's IP ownership, trademark ownership, copyright on the game itself. If any of those three are owned by Nintendo, then it's legally equal to an outright first party game where Nintendo controls all three aspects, because Nintendo gets to make the final call on which platforms the game can appear on.
Publishing duties don't mean anything, hence why DQ XI, Octopath Traveler and Daemon X Machina remain in the third party category.
Snipperclips, MUA3 and Astral Chain all have Nintendo's copyright on them. The Marvel IP obviously does not belong to Nintendo, but the game MUA3 does (same situation as Spider-Man on the PS4 where Sony owns the game, but not the Spider-Man IP). Astral Chain was co-developed by Nintendo as opposed to Snipperclips, but in the end it's first party all the same.
Mario + Rabbids is a collaboration between Nintendo and Ubisoft, and Ubisoft can obviously not do what they want with the game because the Mario IP on its own is already not theirs. It's the same thing as Pokken (with Bandai-Namco) and Fire Emblem Warriors (with Tecmo-Koei). All of those games have regional differences in who handled the publishing, but ultimately they belong into the first party category because none of the third party partners have control over the games, unlike in the examples of DQ XI, Octopath Traveler and Daemon X Machina which appeared on non-Nintendo platforms.
A particularly odd case is the Bayonetta series where Nintendo funded the second and third game which made those two titles Nintendo games (Nintendo has the copyrights for the games, does not own the IP) whereas the original Bayonetta was and is a Sega game. This is why you keep seeing the first Bayonetta get ported to non-platforms (most recently in a Bayonetta + Vanquish package), but Bayonetta 2 remains exclusively on Nintendo consoles.