This is just a matter of fiddling with math!
You have to get two values first: the player position and the mouse position.
If your mouse position is relative to the viewport, you'll have to get the player position relative to the viewport as well. If the mouse position is relative to the world, you'll have to get the player position relative to the world as well.
Calculate the x- and y-difference between the two points (which can be done using a vector). Now you have the vector from the player towards the point the mouse is at.
Now all you have to do is calculate the angle between the horizontal vector and the vector you just calculated, and update the rotation of your player according to that angle. Do this every tick in the _process() function, and you will have the result you want.
To show you how to calculate the angle, I will use vector math, and in particular a concept called the dot-product. You can read more about it here: https://socratic.org/questions/how-do-i-calculate-the-angle-between-two-vectors
Alright, on to the code!
You might have to fill in some additional stuff, such as the method how you get the mouse position or the player position, but this is how the math should work:
# Get all values.
var mouse_pos = Vector2(x, y)
var player_pos = Vector3(x, y, z)
var delta_x = mouse_pos.x - player_pos.x
var delta_y = mouse_pos.y - player_pos.y
# Calculate angle here:
var dot_product = delta_x * HOR_VECTOR.x + delta_y * HOR_VECTOR.y
var mag_touch_vector = sqrt(delta_x * delta_x + delta_y * delta_y)
# The 1 in below calculation is the magnitude of the horizontal vector,
# which is always 1. You can leave it out if you want.
angle = (dot_product / (mag_touch_vector * 1))
# Now update the player rotation:
self.rotation_degrees.y = angle
If something isn't working, don't hesitate to ask about it!