Questions about door locks

Hello
I would like to buy a lock for my front door, and I am researching to make a good purchase.
Looking through the specifications I saw that one detail is not specified.
My lock does not have an outside opening handle, the handle is only inside.
Turning the key, after the second turn, the last quarter turn opens like a handle, and then returns to the upright position with a spring.
I don't know if this is a common feature, I am not a lock expert.
I'll add a diagram to explain better.

To open my door an automatic door lock would have to make 2 1/4 turns and then allow the spring to bring it back 1/4 turn.

Do automatic locks handle this ?
Thanks to all

Found