I’d probably use a mix of both approaches. A single campaign can keep the branding and release message consistent, while separate targeting lets you adapt the promotion to markets where the genre has stronger potential. I’d start with a few priority countries, test playlists, blogs, social channels, or ads, and compare the quality of engagement from each market. If one audience responds particularly well, the campaign can be adjusted around that data. When comparing services, music promotion packages can also be useful for seeing which promotional channels can be combined.

Would you actually split the budget between countries from day one, or start small and see where the song gets the most attention before spending more?

I’d start small and watch the response. If listeners in one market show stronger engagement, I’d put more of the budget there instead of spreading it evenly.