Music on iPhone isn't visible in Google Play Music app
I feel like what was actually happening on Android is that it was uploading files from your library to the cloud and then making them available in Google Play Music (one of its major features). It also could have been reading the music library on the device directly. I'm not completely sure, to be honest, but for purposes of this answer, it's mostly irrelevant.

For iOS, though, you will need to upload the music to Google Play Music using the Google Play Music Manager on your computer. Once that's done it will be available on Google Play Music on your iOS device (and Android, for that matter).

Otherwise, you would need to use the iPhone Music app to listen to the MP3s you synced onto your iPhone, or another app that supports directly using those MP3s.