Since Apt Sangam is proprietary, you usually get it via:
: Created by Adobe Originals for exemplary design quality and aesthetic longevity. 💻 Digital & Modern (Sans Serif) apt sangam tamil fonts top
If you want the most stable, standard experience, is the package you are looking for. It carries the legacy of Tamil computing on Linux. However, for a cleaner, modern look, I highly recommend installing fonts-noto-core alongside it. Since Apt Sangam is proprietary, you usually get
sudo apt install fonts-rachana
Headlines, banners, and emphasis.