Emulation

If you don’t feel like going through AltStore for Delta, provenance, or etc, a fun alternative is Eclipse Emu. You can download it as a web app!

I used to keep an ear open for any apps with hidden emulators to sneak through the App Store, but it seems like that hasn’t happened in a long time and the ones that exist all seem to be incompatible with newer phones. (Plus, you need to jump through hoops these days to carry over delisted apps to a new phone.)

I also use Provenance sideloaded. Seems like one of the best options for supporting multiple systems and being easy to use/stable. I used to use Delta, but I felt that new systems were being added too slowly.

https://afterplay.io/ Seems like a decent option as it’s a web app, so it requires neither sideloading nor jailbreaking. But you need to get premium in order to access some systems.

I have iDOS 2 from the App Store on my phone. (It might be available still in some regions, or you can sideload it.) While I never had any DOS experience from back in the day, it’s nice to have a random collection of DOS games available everywhere I go. Launchbox made an easy-to use launcher for DOS, so I can use simulated mouse controls to launch games without having to switch to the keyboard. If you want to torture yourself, you could theoretically emulate retro games using emulators written for DOS in this way.

Not technically emulation, but there’s a copy of Mario 64 rebuilt as an iOS app floating around somewhere. I prefer the controls and screen to Mario 64 on Provenance.

Don't have an iOS so never had to dig in the topic, but maybe it is possible to run emulators inside other emulators? Like how you can play SNES and Mega Drive games through homebrews on the PS2 and, by extension, PS2 emulators.