Thanks for the discussion! I personally noticed that some Duolingo sound clips pronounce a very hearable R at the end of Turkish words, some don't, and most singers (on Kralpop and in recent Turkish Rock and Pop hits playlists on Spotify) and people on the streets of Berlin don't, or at least not in such a way. Further research made me discover this elaborate Quora post stating, like @MustafaOuz526752 wrote, that there is a tendency to omit the final R, and that they perceived it as a typical "state TV news announcer in the 1990s" style that would get you noticed in a negative way if you spoke like that in İstanbul today.
That sounds like good news for me, because, as a German, I have always struggled to pronounce the final R in that (in)correct "Turkish" way.
Maybe someone who lives in İstanbul and who is no native Turkish speaker can confirm or disagree?