I'm going to say it, I think that Google's Noto Color Emoji set are ugly.
First off, emoji designs are wildly inconsistent. Numerous different art styles are used throughout the emoji set. The face emojis are consistent, but the rest are just, ugh. Take, for example, the pig and unicorn emojis. The unicorn has lighting, while the pig doesn't have much of it at all. And the dragon uses gradient shading, when almost none of the other emojis do. Only some animals, such as the fox, have highlights in the eyes. And the wave uses outlines. The grinning and cat grinning look like they belong to completely different emoji packs. I could go on and on about this.
This one is more of a personal preference, but I just don't like the designs of them. Something feels off about the face emojis, and the gradient they have just looks hideous. Maybe it's the imperfect circle shape they have. I don't know. Something about them just makes me want more. I will say that I like the original redesigned set from Android 8, but Android 11 took the charm out.
I would even argue that the original Noto Color Emoji set before the Android 8 redesign is even more iconic, at least the faces. The blob emojis are so fun, and although I personally don't like them, many more people do. Many people still use custom variants of the blob emoji set on platforms such as Discord.
Now, this wouldn't be a problem, except for the fact that so many projects use these emojis. The Noto Color Emoji are open source, so anybody can use them in their projects. But there are so many better emoji sets to use. Twemoji may be a little overused online, and Elon Musk fired the entire team behind the original set, but there are forks still maintaining Twemoji that I would take over Noto any day. Microsoft's Fluent Emoji are another good pick.
Finally, I will say there is one good thing that has come out of Noto Color Emoji, and that's Emoji Kitchen. If you use Android and have the official Gboard app, you can simply select two emojis and it will combine them, and there is a lot of charm and detail in some of these combinations. If you don't have Gboard or an Android device, you can also just Google "emoji kitchen" to be able to play with them there. It's honestly a lot of fun, and I would highly recommend checking it out.