Can I buy or play offline music tracks from the iTunes Store without subscribing to Apple Music?

Yes, you can buy music from the iTunes Store without an Apple Music subscription. See the following: Buy or download music from the iTunes Store in Music on Mac - Apple Support

or

Buy music from the iTunes Store on your iPhone or iPad - Apple Support

If you are asking about iTunes Search in the Music app on a Mac running macOS Catalina or later, the following may help:

In the Music app menu bar, choose Music > Settings or Preferences > General and insure Show iTunes Store is selected.

Then click in the search box at the top of the left sidebar and then click the iTunes Store option at the top right of the main window as shown in the example in Buy music from the iTunes Store on your iPhone or iPad - Apple Support

If the 3 options don't appear at the top right of the main window after doing the above, 2 things to try:

1) If the View menu in the menu bar contains "Hide Playing Next" or "Hide Lyrics" then click that item so that it changes to "Show Playing Next" or "Show Lyrics."

2) If there is a very small < at the top left of the main window (to the right of the sidebar search box), click it one or more times until there is no < there.

To learn how to buy music from the iTunes Store click here --> Buy music from the iTunes Store on your iPhone or iPad - Apple Support

I had exactly the same question. I do not want to sign up to Apple Music I just want to continue to be able to purchase online music.

CBZort wrote:

I had exactly the same question.

Please follow the exact same answer.