To add AzureLib to your project as a dependency you need to add the following to your build.gradle (NOT THE BUILD SCRIPT):
How AzureLib gets added to your dependencies varies based on modloader and setup.
The Gradle property MCVERSION should be something like 3.0.0 with the Mod's version.
The Gradle property MODVERSION should be something like 1.21.1 with Minecraft's version.
Here are common dependency setups for different loaders.
For Forge Gradle users, you will need to enable Mixin refmaps in your client sourceset. This can be done by adding 2 lines inside of your client runs, to look like below.