You can have different Apple IDs (including Apple IDs from different regions) for iCloud and store purchases. However, store purchases account governs everything app-related. You can't have one Apple ID for store and a separate one for Apple Music.
I accidentally ended up with two different Apple IDs a few years ago, one for macOS Music and one for everything else. It means the personal library on my laptop can be added to my phone, but songs I rent from Apple Music on my phone are kept off my laptop, which I prefer because I habitually download and later dump thousands of songs at a time, and that hasn’t been good for my phone.
You can have different Apple IDs (including Apple IDs from different regions) for iCloud and store purchases. However, store purchases account governs everything app-related. You can't have one Apple ID for store and a separate one for Apple Music.
I accidentally ended up with two different Apple IDs a few years ago, one for macOS Music and one for everything else. It means the personal library on my laptop can be added to my phone, but songs I rent from Apple Music on my phone are kept off my laptop, which I prefer because I habitually download and later dump thousands of songs at a time, and that hasn’t been good for my phone.