While this super sucks and is a loss for the wider Emulation community, I think this is the first time where I can actually see where Nintendo is coming from in one of those legal dilemmas.
(Disclaimer: Not a lawyer, some of this is hearsay. I'm only an avid reader, but haven't actually ever done any switch emulation myself. Keep your salt grains ready and correct me if I share wrong information please.)

Yuzu appearently raked in 30k USD per month on their patreon. And many of these patreons were most likely not just donating out of good will and with a "Thank you" mindset, but they were actually in it for the supporter/early access builds, which were time-gated behind these subscriptions. This automatically raises an eyebrow for me. ~~Second problem, one of these early-access branches appearently had optimizations for running Tears of the Kingdom, even before it officially released (the game got leaked 1~2 weeks early). This meant, for a short period of time, the yuzu emulator was the only way to play Nintendo's game (besides using a homebrewed switch) and I think this put them in a direct competition against Nintendo.
That is just an absolute no-go when you're trying to provide legal and safe emulation. This basically invites pirates with a big welcome mat.~~ Correction: I just found out, official yuzu builds never ran TotK pre-release. It was modded versions through 3rd party devs.

The core idea of "good" emulation is video game preservation and the right, to do whatever you yourself want with your property.
The yuzu devs in this scenario seemed like they were trying to make a profit off of giving early access to someone elses copyrighted work. And that does sound pretty illegal to me.

What Nintendo is trying to argue in their writing doesn't super resonate with me though. yuzu emulator needs a file from the switch OS called "prod.keys" in order to decrypt and to actually play switch games. Nintendo argues that any attempt at extracting this file is "circumventing digital copyright millenium act", and therefore yuzu is facilitating piracy because it ONLY works with this file. This also seems to be the reason why they went after the tool that is used to extract prod.keys, called "Lockpick" earlier last year.

I don't think using a program to obtain your own keys from your own property should be illegal. While sharing those files might very well be.

Overall, very iffy topic, just a reminder to any Emulation Devs to always take the safe route whenever possible. In my personal opinion, I don't think developers should even try to emulate any games that are newer than ~1 year, as a show of faith that there is no monetary incentive.