My question is regarding the very tinok shinoshba jews today who were raised with basically no real Torah. Are they damaging their souls by their actions, which are many things forbidden by the torah, even though they likely dont even know much is forbidden?

Their souls are definitely missing out (that's the literal translation of the word: cheit) on those mitzvot which they're not observing, but they obviously are not punished nor held accountable for that which they are unaware.