"no lags, no sound problems, no glitches"
Good luck with that on handhelds outside of FPGA clones and true clones.
It is a matter of degree though. Sound problems rarely get to gamebreaking levels, however if you are a golden ear type that can spot too slow decays or something along those lines and have been playing on bsnes/higan for years then you might find SNES emulators sub par. On the flip side you can play most of the library, special chip games largely included, just fine.
Similarly most emulators were 90s C emulators tweaked to run on the PSP and are much as you might expect from that (PC emulators of the time of the PSP going far more down the high resources, high accuracy path as well as dynamic recompilation) rather than being built from the ground up.
http://psp-news.dcemu.co.uk/emulators-for-psp-1158256.html is fairly complete and a reasonable jumping off point.
To that end the PSP experience tends to be most mainstream things up to the 16 bit era work more than well enough to play them and be able to seriously discuss the library or shift to the real thing (controllers aside) quite easily, and also the PS1 (more on the injection side of things than homebrew emulators, though homebrew injection and fiddling does well) plus the actually surprisingly solid commercial library. Homebrew that is not emulators or ports of things you might expect to see on
https://osgameclones.com/ is not as shiny as we saw on the GBA and DS but has a few interesting things; wagic (a magic the gathering... call it engine) being far more advanced on the PSP than the DS equivalent, and I will note many of the ports of things that got source releases (Doom, Quake, Duke3d...) are actually pretty solid compared to their DS contemporaries which were far more involved and in terms of mods limited porting efforts.
http://psp-news.dcemu.co.uk/psp-homebrew-games.php for a start of a list there,
https://www.gamebrew.org/wiki/Category:PSP_Homebrews having a lot as well.
No PC emulation particularly worth speaking of (don't imagine 486 or contemporary to the PS1 dosbox, yes technically windows 95 boots but it is not a game playing machine) and if your requirements are those listed it would be a stretch to say look at the N64 (fantastic effort, buy the coders a beer if I ever meet them sort of thing, but not a player's thing for most games). I did less of the arcade side of things so can't say much there, and the Japanese non sega-nintendo consoles languished a bit compared to some of the efforts put into the SNES and megadrive/genesis.
Also regarding never used. It has been long enough now that I might be concerned with the battery if it has sat on the shelf discharging for all this time.
