I don't understand my own movment code, can you help me out?

Audiobellum Add comments to every line in your player movement code, describing your understanding of what is happening in that line. Post that commented code up for discussion.

Audiobellum
Nice.
Firstly, just a stylistic remark; there's a widely accepted convention to place comments above the block/line they refer to, or at the end of the line. As a general advice, get into habit of commenting as much as possible. It makes code more readable and easier to get into for other persons as well as yourself after not seeing it for a long time. When implementing an algorithm it's often a good approach to first write the whole function/class just as a series of comments, and then implement the actual code piece by piece, leaving relevant comments in place.

From comments in your code it seems that the only thing you actually don't understand is basis and how it's used for calculating the velocity vector.

Basis is a collection of 3 vectors. Each of those vectors is one coordinate axis of your object's local coordinate system. The basis is needed to represent the orientation of an object in 3D space.

You can visualize it like this:

Make the depicted gesture with your right hand.
If the hand is your object then each finger represents one of it local coordinate axes: x, y, and z. Those coordinate axes are the basis vectors. The length of each basis vector is always 1.0 (i.e. they are unit vectors)

Imagine that your room is the global space. If you align your fingers with the room walls then the basis vectors will be the same as global coordinate system axes; your x basis will be (1, 0, 0) etc...

However if you rotate your hand into any other random position, then your basis vectors may become some arbitrary vectors (in respect to global space of the room).

Now if you want to tell your hand to move in the direction of your index finger, the velocity vector will need to be aligned with that index finger, meaning the velocity vector should be set to have the direction of your basis x vector, and magnitude of the movement speed.

Audiobellum it seems like all your movement code is separated from your main script.
xyz explained it pretty well, so just gonna provide another script.

extends CharacterBody3D

var speed = 200
var gravity = 40

func get_input(): 
	var input_vec : Vector3 #create a vector3 and assign each direction to it. (
	if Input.is_action_pressed("forward"):
		input_vec += Vector3.FORWARD
	if Input.is_action_pressed("backward"):
		input_vec += Vector3.BACK
	if Input.is_action_pressed("left"):
		input_vec += Vector3.LEFT
	if Input.is_action_pressed("right"):
		input_vec += Vector3.RIGHT
	input_vec = input_vec.normalized() #normalize it so going diagonally doesn't go faster 
	input_vec = input_vec.rotated(Vector3.UP, rotation.y) #rotate the input vec depending on the rotation of the player 
	return input_vec #return the vector

func _physics_process(delta):
	if !is_on_floor():
		velocity.y -= gravity * delta 
	velocity = get_input() * delta * speed #velocity is a vector3, you add delta and some speed to it to control it how you want 
	
	move_and_slide() #call move and slide at the end

Audiobellum
I guess my explanation wasn't really understood

Your forward vector should be one of the basis vectors in object's global transform. You decide which one. That vector is already "properly" rotated, so no need to do any additional rotation. Just take that vector. You can normalize it just in case the object is scaled. It really takes only one line of code to calculate the forward velocity vector.

There isn't any visible movement probably because you multiply your velocity vector by delta. Delta is typically a very small number. This makes velocity magnitude small as well, resulting in object barely moving

Besides, according to movement equations in physics, velocity multiplied by time equals distance travelled. You only need to specify the velocity. The distance travelled is calculated/applied by move_and_slide()

Audiobellum Don't touch the position. That's move_and_slide() 's job. Also you'd typically want to take the basis from global_transform, not transform. But this really depends on your node setup. And make sure move_forward() is actually called from _process() or _physics_process() as others have pointed out. Put a print statement in there just to be sure it's called.

Audiobellum There's likely a problem with your setup. Try to do this in a clean project with just a couple of nodes, without any state machine stuff.