LIUWEI New Retro Gaming Console & Game Stick Pro - 20,000+ Classic Video Games, 23 Emulators, Dual Wireless Controllers, 4K HDMI Output, Plug & Play, Compatible with TV, PC, Projector, 64GB

Don't expect HDMI game sticks to play PS2, it's just not powerful enough. You could go for something like this https://www.amazon.com/-/es/LIUWEI-Nueva-consola-juegos-retro/dp/B0GVCLN3MS although at this point you might as well go for a rather cheap ha dheld like an RG40XXH IN AliExpress. I have both of them and I must say I'm happier with the handheld