You don't drop the BIOS file into PCSX2's folder. Instead, you point PCSX2 to the BIOS file location via its configuration dialog.
SCPH-XXXXX.BIN (~4 MB).portable.ini in PCSX2 dir → BIOS path stored relative to exe.BIOSDUMP tool (or dumper.elf).SCPH-XXXXX.BIN to USB → PC.Requires: PS2 (fat or slim), memory card (8 MB+), FreeMCBoot install method (disc swap, modchip, or bought card).
Once configured, PCSX2 will boot PS2 games directly. No BIOS in install folder needed—just a configured path.