Maybe not, but to me one of the defining features of turn-based is that the game does not go if you are not playing, or taking your turn so to speak. The rounds are similar enough in function to super auto pets, and those feel like turns to me so I just lumped them in together.

Very rarely. Pokémon and Expedition 33 are the only ones that come to mind outside of more casual games like Super Auto Pets or Balatro

Dead Flag Blues calls to me more and more every day