Zoro's attack not only scarred Kaido it caused him to start breathing heavy and huffing. He wasn't huffing before.
Yes, Zoro did that.
The scar he gave Kaido means Kaido has a injury that can be agitated or taken advantage later on. You can try to downplay it all you want by calling it a superficial injury but the truth is nobody else's been able to repeat Zoro's feat.
You don't understand how attack power, injury or endurance works. A character strongest attack will always be their strongest attack at the time they use it. That means if they use it at 100% it is their Strongest attack. If they use at 20% it's still their strongest attack because their second strongest attack is still going to be only at 20% strength.
When Luffy used his strongest attack to defeat Doffy both of them were in a weakened state.
Zoro is a character that uses incredible physical strength with his attacks. With 20-30 broken bones his physical strength would be greatly affected. Law didn't even think he should be able to move. That tells you how much weaker he was.
We know from the manga part Zoro's growth in Wano was increasing the control/size/strength of his barrier haki. That's beneficial because it allows the user to produce stronger attacks with less physical strength. IE: Zoro cut a cliff with barrier haki using only the physical strength needed to cut a tree.
An example of Zoro using his incredible strength with large powerful barrier haki was when he cut the Giant skull horn.
That attack cut the horn from that distance and shook the entire Island.
If Zoro wouldn't have been in a weakened state and could have used his full physical strength to further power up his Dead Man Game attack it would cause easily 2 to 3x more damage to Kaido. It would have either defeated him or dropped his strength by over 70%.