Dunno when/how a game is classified a classic, but since PS2 is from the 6th gen, guess I have some suggestions! =D
Ultimate Ninja 5 is pretty cool, I think. Don’t like the anime much, but gameplay loop still feels pretty good nowadays. Only released on PAL and NTSC-J regions, though.
Dragon Ball - Budokai Tenkaichi 2 is also pretty fun, coming from someone that also doesn’t like the series it comes from.
I guess Godzilla: Unleashed could count as fighting game too? If so, I recommend it too.

I don’t mind necro as long as it isn’t obvious spam, so don’t worry. =D
(besides, Reddit also had a lot of this, where pertinent replies would only appear a long time after the posts were made)

But thanks! The game looks pretty interesting, going by the promotional materials, and the store page also mentions it has both English and Japanese, so likely at least texts will be translated.

Oh. Oopsie. e.e"

Just checked. Initial release was in 2016. Maybe I confused it with a previous title from IF/CH.

Yup, like this!

Grid-based, dungeon crawler RPG (a mouthful, I know). The most recent titles in this genre I remember are the Mary Skelter trilogy, but the first game is about 10 years old already.

If you absolutely must get something from Google Play, I suggest Aurora Store, which acts as an alternative frontend for Google Play, so you don’t have to have GApps installed.

If you have use for command line programs, Termux, a terminal emulator, is a great option, and it also works with root.

For reading eBooks, I also have a recommendation, Librera Reader (but I’ll check the OP’s recommendation too).

Material Files and Simple File Manager are great file browsing tools. But if you need a file browser for root specifically, I recommend Material Files specifically.

Plus a surprisingly decent CBZ/CBR reader, if you like reading comics in a TV.

Modded PS Vita, since upon modding, its scope of playable games becomes ridiculously high. Native games, PSP and PS1 games supported natively which can be expanded upon modding with homebrews and back ups of official releases you paid for, plenty of emulators for both the Vita and the PSP, wrappers for Android and PC games, as well as ports of game engines, getting released pretty much every week, and OS extensions for forwarding the Vita’s screen to another device, making certain bluetooth controllers compatible, fixing/improving the system, and so on and so forth. It’s a nice console. :3

Besides GOG, which has been mentioned in other comments, there’s also Zoom Platform (basically Good Old Games 2.0) and Project EGG {Japanese store/kinda preservation project (kinda since it uses some basic DRM) for games mainly from non-MS-DOS PCs}.

DRM is not a protection. It is a killswitch. Even MMOs can theoretically be DRM-free. So this situation just lays the DRM issue bare. points to GOG, Itchio, ZP, and so on