Generally there are four approaches to taking screenshots, maybe five depending upon how you want to view things.
1) Just emulate it.
Tricky if the emulation is weak (and PS2 stuff is good but far from mature as 16 bit, older and equivalent 2d focused things), some purists might not accept it, and even if the purists don't matter you might have to disable options lest you end up with a fancy upscaled (if not high res "natively"), smoothed (inter image and intra image), texture replaced, massive draw distance bump... type super image. Emulation can also cut the other way and sometimes you want the failures
http://bogost.com/games/a_television_simulator/
2) Some devices will have options. This tends to be for newer devices where they have an OS running in the background that can grab a framebuffer. PS2 is unlikely to be this but looking at above there might be a means, or might be a means to hook things; cheats also appreciate an OS running in the background that can poke at things, though it is often possible to leave/alter code as things start to leave something resident in there, would then be possible to do that to grab a framebuffer or something and dump it as something on whatever means available (memory card, network, USB maybe, bitbang over a LED/sound cord
https://gbatemp.net/blogs/dumping-gameboy-games-the-insane-way-part-1.14244/ , some external tool but more on that later).
2a) For developers, suitably blessed magazines and such then there might well be a specialist device that acts as a capture method. Might be one of the others on this list, might be something above and beyond stock hardware (dev grade gear having more RAM and such like for this sort of thing).
2b) For some really old devices like the old home computers (vic20, commodore64, amstrad, atari...) then there could be extra options to dump things but sold as devices.
3) "We have the technology, we can rebuild him".
Devices will not operate in TV signals internally and somewhere in the chain things will be converted into TV signal. Tap that point up the chain and while you might face some of the issues mentioned in 1 it becomes far easier to stick it to something more modern/available in the average nerd's desk. Back then programmable devices to do much might have been nation state, university and international company affairs but all these years on it might well be doable on the my first FGPA/CPLD/raspberry pi/whatever kit.
Most usually associate this more with handhelds where you tap a screen and decode its contents but the principle applies to everything.
4) Traditional capture approaches.
PS2 is old so no fun HDMI out of the box here. Dip back into old school RF, composite and maybe component depending upon what goes (maybe you are playing this on a BC PS3*), possibly sourcing new cables (chances are the stock cables of the day were RF or maybe composite because nobody had a fancy TV) or indeed fiddling with hardware (the N64 RGB mods being a good example, at least until you look into the price of RGB capture..., original xbox VGA mods are also interesting in this, though VGA capture... ouch). You might also have fun things like interlacing (varies from game to game, region to region -- the original xbox had no HD and thus some games with progressive scan officially in PAL regions but software mods exist today).
*the purists, which may collide with speedrunners, can have opinions here as well, or consider it a separate category.
Hopefully you are not wanting to do this for a multi screen type setup
https://forum.digitpress.com/forum/...2-iLink-compatible-games-Network-adapter-LANs