I'm trying to make breadboard circuit with my Raspberry Pi Pico and I'm not sure if I have to push it entirely in the holes or it's good at half?
If you have have the chance please look "inside" a breadboard, every row has 5 metal "clips" that will "hug" pins when they come in. Such clips are positioned on top of the assembly, close to the entrance hole.
That said, you could insert pins as shallow as say 2mm, already making some electrical contact; but that doesn't mean good/safe contact. As other have pointed you will be safe pressing and inserting pins as deep as they go.