Here are the key points I understand from your request:

Write a Blender Python script
The script should render the current frame as a normal map
The normal map should be normalized to look like a typical normal map
You provided an example image of what a normal map should look like
To render the current frame in Blender as a normalized normal map, you can use a script like this:

import bpy

Set the render engine to Cycles
bpy.context.scene.render.engine = 'CYCLES'

Create a new image to bake to
image_name = "Normal_Map"
image = bpy.data.images.new(image_name, width=1024, height=1024)

Create a new material and assign it to the active object
mat = bpy.data.materials.new(name="Bake_Mat")
bpy.context.active_object.data.materials.append(mat)

Enable use of baked normal map
mat.use_nodes = True
nodes = mat.node_tree.nodes
texture_node = nodes.new("ShaderNodeTexImage")
texture_node.image = image
texture_node.select = True
nodes.active = texture_node

Set bake settings
bpy.context.scene.render.bake.use_selected_to_active = False
bpy.context.scene.render.bake.use_cage = False
bpy.context.scene.render.bake.cage_extrusion = 0.1
bpy.context.scene.render.bake.type = 'NORMAL'
bpy.context.scene.render.bake.normal_space = 'TANGENT'
bpy.context.scene.render.bake.normal_r = 'POS_X'
bpy.context.scene.render.bake.normal_g = 'POS_Y'
bpy.context.scene.render.bake.normal_b = 'POS_Z'

Bake normal map
bpy.ops.object.bake(type='NORMAL')

Save the normal map image
image.filepath_raw = "//normal_map.png"
image.file_format = 'PNG'
image.save()

This will bake a tangent space normal map of the current frame, normalized with the typical blue as the Z direction. It will save the normal map as "normal_map.png" in the same directory as your Blender file.

Let me know if you have any other questions! I'd be happy to explain or modify the script further.