Problem with Tamil Fonts

Hello all
Can someone please help me. I have designed a book that is now also published in Tamil. The layout works fine with the font „Baamini“. But now I have been asked to layout everything in a Unicode font (e.g. „Latha“ or „Noto Sans Tamil“). Unfortunately, Baamini is not a Unicode font and I simply cannot manage to install the two fonts „Latha“ or „Noto Sans Tamil“ correctly. Only (pink) rectangles or latin letters appear (see screenshots).
Does anyone know how I can solve this problem? I would be very grateful for any helpful tips.
Barbara
