While not exactly "5.1," Apple Music uses , which is object-based surround sound (better than 5.1). They have a massive library of Tamil songs (Anirudh, A.R. Rahman, Harris Jayaraj) mixed in Spatial Audio. You can subscribe for a monthly fee and download for offline listening.
: While it doesn't support Atmos in the same way, there are curated playlists titled "Dolby Atmos Tamil" or "5.1 Surround" that feature tracks recorded with high production value.