RetroArch (https://play.google.com/store/apps/details?id=xyz.aethersx2.android) for ps2 directly on phone works better but you might encounter issues as it also requires a bios image
How bout u download SMB-SE (Super monkey ball : sakura edition), it can be downloaded without an emulator because sega launched on play store: https://play.google.com/store/apps/details?id=com.sega.monkeyball&hl=en_US&gl=US
Well, finding emulators for those consoles is hard even on PC, but I think I've found a website that lists Android emulators for old consoles: http://hyperspin-fe.com/forums/topic/25159-android-working-systems-list/
I took a quick look and I saw some of the emulators for the consoles you mentioned
I can't help you anymore because I'm too young to even know about those consoles.
you'll probably have to use one of the telescopic controllers that turns the phone into a device similar to a nintendo switch... something like this: https://www.amazon.com/Flydigi-Controller-Bluetooth-Telescopic-Connecting/dp/B07TD4K8HZ as they can typically hold larger phones and tablets.
The ones that are shaped like a normal controller with a phone holder above it (this style) typically can't fit the larger devices.
you're probably right that this is due to the way the emulator creates an ad hoc network connection to pass internet into the emulator
Maybe a different emulator would work better? What are you using? I like Memu the best, but Nox, Amiduos and Bluestacks are other options that you could try, but I'm pretty sure you'll encounter the same issue
you could also try a different mirroring app. Microsoft released one that might work: https://play.google.com/store/apps/details?id=com.microsoft.appmanager but the screen mirroring option isn't available for all devices.