I'll throw my hat in and say my favorite console for Square/Square Enix is the PSP. Most people would rightfully say that the PS1 or PS2 (the SNES and DS are also valid answers) was when Square was at their creative peak and objectively those systems are far more stacked, but my fondness for the PSP makes me wanna give that system the nod over anything else.
The PSP's elevator pitch was "A scaled back PS2 in the palm of your hands" and very few developers can be said to have met that standard than Square Enix. While a lot of studios settled for scaled back versions of their existing IP, Square really did their best to make sure that franchises like Final Fantasy and Kingdom Hearts felt like you were getting some long-lost console experience on the go with minimal compromises. Dissidia is also undoubtedly my favorite spin-off game for any franchise and it is amazing to me that Square Enix casually made one of the most unique, feature-packed and addicting arena fighters on their first try and just haven't bothered replicating that magic since, going so far as to hand the 3rd Dissidia game off to Team Ninja instead. My love for SRPGs also started on this system thanks to the at-the-time best versions of legendary games like Tactic's Ogre and Final Fantasy Tactics. When it comes to expanded ports though, to this day it is debatable that the best version of games like Final Fantasy I, II, III and IV are on the PSP and until First Departure R and Second Story R released on modern platforms the best versions of Star Ocean 1 and 2 were also on the PSP!
Even lowkey releases like Crystal Defenders and Lord of Arcana won me over. The former is a super fun tower defense game that oozes charm and remains the only game in its genre to rope me in that isn't in the Bloons series. The latter is a fairly flawed game chasing after Monster Hunter's absurd levels of success that failed to have levels of a combat system as wonderfully crafted as Capcom's masterpieces on the same hardware. Still, I spent plenty of time grinding away in LoA and the setting/story premise were among the better in that style of game, as little as that matters. Highly recommend anyone interested in LoA to give the expanded version - titled Lord of Apocalypse - out. It adds some content and streamlines some progression while giving combat a bevy of tweaks to help it flow better. I hate numeric ratings but to illustrate how much it improves the game, I'd say Apocalypse takes the strong 5 out of 10 base game into strong 7 out of 10 territory. For reference anything I give a 5 or above is something I enjoy.
It was also the system that introduced me to Valkyrie Profile thanks to the Lenneth remaster, though it is a more controversial release when it comes to if the PS1 or PSP version is overall better. Itadaki Street also got some love on this system and while I've only played this version and the Wii release of Fortune Street I still prefer the PSP release more!
They even have some hidden gems under their belt despite being such a massive publisher. I mean really how often do people talk about Thexder Neo despite it being such a sick as hell side scroller! Playing in a mech that can switch from an on-foot to a flying mode on the fly is pretty novel for that type of game and it works brilliantly.
And ya know what? I fuckin love The 3rd Birthday. It was admittedly the first Parasite Eve game I played and my least favorite of the trilogy, but I think it's a solid-if-basic third person shooter with a neat story that does some pretty interesting things thematically.
As a total side note, it was also one of the systems they crammed some of the saddest entries in their respective franchises into. Crisis Core, Dissidia 012, Birth By Sleep, 3rd Birthday and Type-0 are all stories about doomed protagonists fighting against fate only to inevitably fail. I don't know what was goin on with Hajime Tabata at that time, but dude was really making me cry with almost every release of his in that era lol.
I wanted to go a bit harder with the formating and diving into the games with a bit more depth, but for this thread's purposes this will do just fine. Not expecting to convert anyone to thinking the PSP is their best system cause like I said I know there are 3-4 other consoles that best it by almost every metric. But pound for pound it is my favorite library of theirs even if a lot of that is fueled by nostalgia.