How can I transfer purchased Apple Music on my iPad to an external hard drive?

Sounds like the Google AI system is giving you nonsense answers that do not apply to the iPad.

A Mac can have multiple Music libraries, and holding down the Option key while launching the Music application is how you get to the screen to create a library or select among libraries. But this is not relevant to the iPad or to your task.

As far as copying purchased music out of the Mac version of Music, so you can, e.g.,, put it onto a USB flash drive for the benefit of a car stereo, just open the Music application on the Mac, select songs in the Music window, and drag-and-drop them to the Finder.

The Music database on an iPad is in a hidden area. I'm pretty sure that it is set up to keep you from copying stuff out of it.

In the original Mac / iPod / iTunes model,

• Copying was one-way, from a Mac to an iPod
• There was no easy way to get at the music on the iPod (by design) – to prevent you from using the iPod to copy music to another computer.
• An iPod could synchronize against only one Mac at a time. If you synchronized against a new Mac, that erased all of the music previously stored on the iPod.

That is what formed the basis for how things work on the iPhone and iPad.

Basically, you need to go back to whatever computer (Mac or PC) you used to load the purchased music onto the iPad, and copy the music from there.

If you purchased music directly from the iTunes Store using the iPad, redownload that music to your computer:

Redownload music from the iTunes Store on your PC - Apple Support

Redownload music from the iTunes Store on your Mac - Apple Support

You cannot transfer music from your iPad to a USB flash drive or another device. At least not using Apple's tools. The system is designed to prevent you from doing that.

As suggested previously, go back to the computer that you used to load the Pad and get the music from there. Or redownload music from the iTunes Store on your computer, if you purchased it from the iTunes Store.

Note that the iTunes Store sells music in the form of 256 Kbps AAC files. Many "MP3" players will play AAC – but if you must have MP3, you will need to transcode the songs from one lossy format (AAC) to another (MP3), which may result in a loss of some audio quality.