"Since when could they do this?"

Since the first fight in FF7, 30 seconds into the game? Party members in FF7 are superhumans to whom bullets are a mild inconvenience. Cloud specifically is also canonically a magically augmented super soldier even by the already ridiculous standards of FF7 human resilience. The game FF7 gives you absolutely no reason to believe that Cloud's body works the same way your body or mine work, and in fact give you a thousand reasons to believe otherwise. To me, it's perfectly believable that superhuman Cloud and his supersword are more resilient than skyscrapers, it seems very consistent with the canon.

But yes, I do get your larger point here, it's difficult to suspend disbelief when the story doesn't provide you with enough evidence of the magic's internal consistency. Personally, "magic man with sword is stronger than skyscraper" is a consistent enough genre convention of fantasy video games that my disbelief is not challenged by it, but I do have many magical details that can break my immersion completely.

(Like, I really want more explanation of why Harry can use Sectum Sempra after reading the words in a book, or how Snape "invented" this spell in the first place -- but I recognize that internal details of the HP magic system are intentionally soft and not made to answer these questions)