Personally, for me PS2 era and older is retro for sure. There is a clear distinction where many PS3 games share similar feeling with modern games, while my PS2 ones feel from a past time. We also still had things like memory cards, altrough obviously not all consoles in that generation do. Still, I would put generations on one line, as most console games where ports of the same game across consoles of the same generation, so then that's the last generation with these kinda old ways of storing. PS2's gen is also the last generation console games where completely different from PC, and in my childhood gaming up to then wasn't mainstream but a nerd hobby, causing it to have a very different community. With the generation of the PS3, all of that changed to modern standards.
PS3 and DS I'm a bit in dubio about. Whenever I feel bored with modern games, PS3 and my (3)DS are on the list of "old" consoles I grab back to (together with PS2, PS1, and recently GBC/GBA which I'd consider retro for sure). On the other hand, at least half the games released on it are games I still play on my PC as "modern games". DS is extra hard, as I barely distinct between 3DS as DS in my mind, unless it's using the GBA port for stuff. After all, I play them on the same console and the transition was quite smooth between the DS models making it not feel like a huge gab, unlike the PS2 to PS3. But at the same time, early DS is much older than late 3DS, which I would consider too new for sure.
Anything after that, modern for sure.
(One of) the biggest tech sites in my country uses "at least two generations old" as definition, making PS3 the last retro generation currently. I like it because it fits my usage, but as said I'm a bit in dubio about actually calling the PS3 retro. It doesn't feel old fashioned enough. I mean, that would technically make Skyrim retro. But that's definitly one of those games that are in my "modern gaming" list on PC and Switch...
I can at least personally attest that PS3 is currently the newest gen where people either think you're awesome for buying it now because they get the fun of old stuff, or stupid because they think the old stuff is crap and only the new is cool. For that reason I would agree to allow it on retro places, as modern gaming places just wouldn't appriciate it at all while people who are already into older stuff do on a somewhat regular basis. But that doesn't make it truly retro per se, and it really should take over or be all you use.