Even JioSaavn, which is focused on Indian popular film music, doesn't do anything special. It's a bit more similar to classical music than American-style pop in terms of organization. Music directors are responsible for the entire album of a film, with singers being brought on for a track or two. So one might want to slice by music director, just like looking at all Bach pieces. It's not quite the case with pop producers, who are usually behind-the-scenes. Fans of Indian popular music often follow their favorite music directors, even if they have little interest in the films the music is a part of.
However, even then, this slight difference is well papered-over by just including the music director in the list of artists who made a song.
Indian classical music, however, has a wholly separate and more intricate form of organization. You'd at least need raga and the properties of the raga (like the dominant rasa & associated time of day), along with the various singers and instrumentalists in the ensemble and their instruments. It would be great to search for "morning"-raga-based Carnatic vocal concerts with the lead singer being Sudha Ragunathan.