The .PUP extension is Sony’s proprietary format for system firmware update packages, also used on the PlayStation 3, PlayStation 4, and PlayStation 5.
This file contains the complete operating system, system applications, security patches, and hardware drivers required for the PS Vita to boot and function. Why Do You Need a PSP2UPDAT.PUP Download Link? psp2updatpup download link
For standard updates, it is straightforward. For downgrading, it requires precise placement in the file system (usually ux0:app/MODORU000/ also used on the PlayStation 3