Hen can't use the Cobra payload (mount as standalone game) you must convert it to PS2classic ISO.bin.enc , mount itand load it with Rebug ISO Launcher (or PS2 classic Placeholder), you can also convert to PKG and play.
Remember, not all the games are compatible with PS2 classic.
Unlike early fat models, Slims & superslims support PS2 games only through software emulation (ps2_netemu).
As the PS2 emulator requires a lot of memory, Sony implemented the emulator as a lv2 kernel replacement. When you load a PS2 game the system reboots into the PS2 emulator kernel and the HEN payload is lost.
In Cobra it works because the FW is patched to execute unsigned SELF and the emulator itself is patched to load the decrypted ISO from hdd0.