GitHub link to Nintendo's claim - all the details you need are here
The emulator forks which are being taken down are as follows:
Despite this, the one fork that continues, and will continue without takedown is Ryubing - by Greemdev. This is created by an original member of the Ryujinx team. It's safe, the code is beyond reproach (and violates zero laws or Nintendo code) and actually brings helpful updates.
Still...shitty news. And more indication that the Switch 2's architecture will be damn similar to that of this current Switch. Them taking emulators down means the upcoming games have a solid chance of being emulatable on release. But...that's my own (and others') conjecture, so we'll see when the time comes.
Emulation isn't piracy and you're allowed to back up physical games you own. That's legally your right.
Technically, you're allowed to make copies for personal use unless doing so requires bypassing DRM, encryption, or some other lockout mechanism.
Emulation is still not piracy and neither is making a personal backup, but if making that backup requires anything more than a standard disc drive or a cart reader then it is a DMCA violation.