You can use the Music app on a Mac without subscribing to Apple Music.
See information in Apple Music User Guide for Mac - Apple Support
I find it useful to click on the "Table of Contents" item in that support article.
Also, if you have difficulty searching for your own music rather than Apple Music, see the following:
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.
Closing and reopening the Music app has also been reported to be needed in some cases.