If you obtained Archicad 22 as a student, the library is typically included in the main installer (download from your education portal). Re-download is available via the same portal.
If you own a license for ArchiCAD 22, yes – it is included. Without a license, you cannot legally download or use it. archicad library 22 download
If you have a valid license or educational version: If you obtained Archicad 22 as a student,
Technically yes, but you will lose new features (e.g., Stair tool improvements, Curtain Wall updates). Always use the library that matches your ArchiCAD version. If you own a license for ArchiCAD 22, yes – it is included