Because Eaglercraft exists in a legal gray area (it uses Mojang assets but no official code), you won't find it on the official Minecraft launcher. Here is the safe way to access the updated 1.20 version.
The Eaglercraft 1.2.0 updated version imports hundreds of new assets: eaglercraft 120 updated
One of the first things you notice in Eaglercraft 1.2.0 updated is the UI. Gone is the clunky, tiny inventory screen. The new build features: Because Eaglercraft exists in a legal gray area