MP3 player?

1. There has never been an iTunes app on an iPad like there is on a computer. The Apps on an iPad have always been 2: The iTunes Store and the Music app.

The original app that could play back mp3s on iOS devices was called the iPod App in allusion to previous devices of that name.

It was later renamed to simply "Music". Current iPads have the Music App installed by default, and it can still play mp3s directly by syncing them from iTunes as you would normally on an iPod.

The music App icon looks like this:

You can sync mp3 to it via iTunes as follows: Sync your iPhone, iPad, or iPod touch with iTunes on your computer using USB - Apple Support

The synced files will appear in the Library section of the App.

Alternatively you can try Apps such as MoliPlayer or VLC if you want to and transfer your MP3s to them using the File Sharing feature in iTunes.

About File Sharing on iPhone, iPad, and iPod touch - Apple Support

As said, the Music app has always been the App to import music (mp3s or otherwise). Apple pushes the purchases and Apple Music features more, but that ability to sync is still there.

Most of the music I have there is music I've synced to it from my computer, and not iTunes purchases or Apple Music tracks.