people with bad taste are always like "yurr hurr The Beach is about zuko and mai and how they're a great couple" while intellectuals know that Actually The Beach is about mining any and all of the untapped friendship potential of this striking exchange
One of the best twist moments in Avatar is when Ty Lee suddenly and dramatically turns against Azula at the Boiling Rock. Azula was completely convinced that Ty Lee would obey her without question forever, but Azula wasn't the only one fooled. Mai is just as shocked when Ty Lee rebels as Azula is. Ty Lee's survival instincts were so sharp that she never let anyone know what she was thinking, not Azula, not Mai, and certainly not Zuko.
Zuko really believed that Ty Lee didn't understand who he was at all. He completely bought into the act that she's just a puppet for Azula, who lives in her "little Ty Lee world where everything's great all the time". But the thing is, Ty Lee is one of the most perceptive characters in the show, and she's excellent at keeping that on the down low, but she sees a lot more of Zuko than he thinks, and a lot of what she sees is very familiar to her.
Overshadowed by prodigious siblings?
Wanting to be acknowledged for the talents you have rather than the talents you don't?
Kept in line by fear?
Spending your whole life bending over backwards to fit the persona the royal family has set for you?
So yeah Zuko. She knows you.
This characterization is definitely emphasized with Ty Lee's acrobatics, flexibility, and ability to hit pressure points. There's a level of subtlety and precision that is required for such skills. She had to know her own body to be able to bend it in such ways, and she has to know other people's bodies to be able to disable them.