"Software-only" downgrades for modern firmware are universally recognized as by the homebrew community. Reliable Resources & Tutorials
PlayStation 4 console modding relies heavily on low-level system exploits. The most popular and stable exploit is pOOBs4, which requires firmware version 9.00. If your console updated to firmware 13.02, running homebrew or backups directly from the user interface is blocked. ps4 downgrade 1302 to 900
You can only revert to the firmware version that was installed on your console immediately before the latest update. If your console went from 9.00 directly to 13.02, reversion will work. If your console was on 11.00, 11.50, or 12.00 before hitting 13.02, you can only revert to that specific intermediate version, not 9.00. or 12.00 before hitting 13.02