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.
The patents on the Game Boy hardware expired years ago, so that's what gives Analogue the right to do what they do. As for these Switch emulators, I have no idea, but I'll guess it's just Nintendo trying to scare people without their own legal departments into complying.