You mentioned "TamilYogi" in your search. While this was a popular site for downloading movies, here is a review of that aspect as well:
For Policymakers and Platforms
Before searching "[Film Name] Tamilyogi," check JustWatch.com/India to see which legal app actually hosts the movie.
– Platforms like Amazon Prime Video, Netflix, Hotstar, ZEE5, Sun NXT, and MX Player (free with ads) offer extensive Tamil film libraries.