Hello Bratkovski,
Thanks for reaching out to the Apple Support Communities. I understand you're wanting to make a purchase from the iTunes Store. From your message it sounds like you're not seeing the iTunes Store as an option in the new Music app on macOS Catalina.
To view the iTunes Store as an option open the Music app > Select Music in the menu bar > Preferences. In the General tab you'll see the first section is about your iTunes Library. Below that section is "Show:" This is where you can select to see the iTunes Store, Star ratings, and Songs list checkboxes. Be sure that the iTunes Store is selected and click OK.
Return to the Music window and click in the search box. Once you've clicked in the Search box look to the right side of the Music window, just below the volume slider. There you'll select if you want to search in Apple Music, Your Library, or the iTunes Store. You'll see a screenshot of how this should look under, "Buy or download an individual item," from this article: Buy or download music from the iTunes Store in Music on Mac.
Enjoy the day!