You cannot play PS2 games on PS3 by simply "downloading PS2 data." The architectures are fundamentally incompatible.
Why It Doesn't Work
Hardware mismatch: PS2 (Emotion Engine + Graphics Synthesizer) vs. PS3 (Cell + RSX). No native backward compatibility via software alone.
Limited software emulation: Only select PS2 Classics (officially ported/emulated titles) were sold on the PlayStation Store for *specific* PS3 models (early 60/80GB fat models with hardware EE/GS, and later Slims via partial software emulation).
Legality: Downloading PS2 ISOs/ROMs without owning the disc is copyright infringement.
Legal Ways to Play PS2 Games Today
PS2 Classics on PS3: Check PlayStation Store on a compatible PS3 (list is short: GTA III/VC/SA, MGS2/3, Dark Cloud, Rogue Galaxy, etc.).
Original PS2 console: Cheap, reliable, plays entire library natively.
PC Emulation (PCSX2): Excellent compatibility, upscaling, widescreen patches. Requires decent PC (modern mid-range) and legal BIOS dump from your own PS2 + legal game ISOs from your own discs.
PS4/PS5: Some PS2 Classics re-released as PS4 titles (trophy support).
Respect copyright—only play games you own legally.