Before you download anything, you must understand how your specific PS3 model handles PS2 games.
If you own original PS2 discs, ripping them to ISO (using a PC DVD drive) and converting them to PKG is safer and legal. Tools required:
Search for “PS2 Classics PKG” on Archive.org. You will find dozens of pre-converted PKG files for popular titles like Grand Theft Auto: Vice City, God of War I & II, Shadow of the Colossus, and Final Fantasy X. These are often uploaded by preservationists.