For 3D nodes, you can access the local axises with basis using this code:
"The Z axis relative to the object's local transform (generally is considered forward vector)"
spatial.transform.basis.z.normalized()
"Same as above, but relative to world space as opposed to local space"
spatial.global_transform.basis.z.normalized()
#
"The X axis relative to the object's local transform (generally is considered the left vector)"
spatial.transform.basis.x.normalized()
"Same as above, but relative to world space as opposed to local space."
spatial.global_transform.basis.x.normalized()
#
"The Y axis relative to the object's local transform (generally is considered upwards vector)"
spatial.transform.basis.y.normalized()
"Same as above, but relative to world space as opposed to local space."
spatial.global_transform.basis.y.normalized()
There is also rotate_object_local and translate_object_local for Spatial as well.
For 2D you need to use something like this (I can never remember which order cos and sin go in. You may need to swap them for the code to work correctly):
Vector2(cos(node_rotation), sin(node_rotation))
The code above will give you a vector pointing towards the node's local X axis. (Add 90 degrees to node_rotation get the local Y axis)
Hopefully that helps. I'm not sure on whether or not Godot will be getting different/easier ways to access the local axises. I do not think there is any plans, but I'm not sure.
