iPods do not have, and have never had, the iTunes app on them.
- iTunes is the programme (application) for a desktop computer and you can use it to buy music from the iTunes Store, and to manage your music library, regardless of where you purchased the music. For Windows computers, or for a Mac using OS Mojave or earlier, you can download it from iTunes - Apple. If you have a Mac using OS Catalina or later, you do not use Tunes; instead you use Finder, which I believe comes already installed on the Mac
- The Music app, which is pre-installed on the iPod, is used to play music stored on your iPod. The icon is a representation of a musical note
- The iTunes Store app, which is pre-installed on the iPod, is used to buy music from Apple, for downloading to your iPod. The ion is a white five-pointed star on a purple background
What is it that you're trying to achieve?