My first cat was definitely a shoulder and lap cat. Pretty much anywhere, but she loved to climb up on my shoulder like a pirate’s parrot when she was small.
My current older cat is definitely a shoulder cat but lacks the back leg strength these days, so I let her anchor herself with her front claws (always with a shirt on).
The best one is my current younger cat, who I carry around like a human infant, back downward, legs in the air.