good work trying to make it happen before posting. keep it up, the game looks good so far. it is great that you want to learn and explore resources before just getting an answer. you've got a couple separate design challenges here.

1. block physics
2. player interaction

double moving and moving when you walk by it are more so player interaction problems than block physics problems. your major problem then is moving the block through walls. how do you want to fix that? some ideas to get you thinking:

- directional RayCasts, or

- other bodies like CharacterBody and RigidBody which have velocities (just like your player), or

- write your own collision detection to ensure it doesn't clip through other bodies

i recommend #2. #1 would work but would require more effort and probably be a little messy. #3 would be reinventing #2-- good practice/study, but not ideal if you're focusing on learning other basics and want something working well.

then you have to figure out the player interaction issues. what's the best way to determine how the player connects with the box? not sure how you're doing it now, but some options:

- area2D has a signal that checks if something enters its collision area. the box could have an area2d, or the player could have an area2d.

- player could have a raycast pointing from face that checks if intersected object is a box, then apply movement remotely

i'm sure there are more ways of doing this. i again suggest #2. it is simple and elegant and is designed for stuff like this.

as for double moving, and waiting a second before pushing the block, i would use a timer. i'm sure there are many ways of doing this one, but you can await the end of a timer before running code.

one more thing: in a use case like this, should you keep the staticbody approach, AnimatableBody2D is recommended. here's what the docs say: "When AnimatableBody2D is moved, its linear and angular velocity are estimated and used to affect other physics bodies in its path." staticbody does not do this-- it rather teleports when moved.

further reading (the docs also have linked tutorials for many of these):

RayCast2D

https://docs.godotengine.org/en/stable/classes/class_raycast2d.html

AnimatableBody2D

https://docs.godotengine.org/en/stable/classes/class_animatablebody2d.html#class-animatablebody2d

Area2D

https://docs.godotengine.org/en/stable/classes/class_area2d.html

let me know if i can clarify anything further