Return to Answer

.name and .type represent the variables of the key_block itself:

["Morph.Upperarms.Shoulder"]

1. 'KEY' (As in "Key' or 'Key.001' in my sample question.)
2. Source Object: bpy.data.objects['Source_Mesh'].data.shape_keys This represents the object containing the key in item 1.
3. Data Path: This represents the exact name you would see were you to copy the shape key as driver and paste it into the "Path" field of the driver editor.

.name and .type represent the variables of the driver being added. .type specifies either a single property (what we're using), a transform channel, rotational difference or distance.

1. 'KEY' used as input for the driver (As in "Key' or 'Key.001' in my sample question.)
2. Source Object: bpy.data.objects['Source_Mesh'].data.shape_keys This represents the object containing the key in item 1.
3. Data Path: This represents the exact name you would see were you to copy the shape key as driver and paste it into the "Path" field of the driver editor.

   import bpy
    
    selected_obj = bpy.context.selected_objects
    selected_obj.remove(bpy.context.active_object)
    
    active_obj = bpy.context.active_object
    shapekey_list_string = str(active_obj.data.shape_keys.key_blocks.keys()).lower()
    
    
    for obj in selected_obj:
        for key in obj.data.shape_keys.key_blocks:
            if key.name.lower().lstrip(obj.name.lower()) in shapekey_list_string:
                if not key.name == "Basis":
                    skey_driver = key.driver_add('value')
                    skey_driver.driver.type = 'AVERAGE'
                    if skey_driver.driver.variables:
                        for v in skey_driver.driver.variables:
                            skey_driver.driver.variables.remove(v)
                    newVar = skey_driver.driver.variables.new()
                    newVar.name = "value"
                    newVar.type = 'SINGLE_PROP'
                    newVar.targets[0].id_type = 'KEY'
                    newVar.targets[0].id = active_obj.data.shape_keys
                    newVar.targets[0].data_path = 'key_blocks["' + key.name.lstrip(obj.name.lower())+ '"].value'
                    skey_driver.driver.type = 'AVERAGE'
                    if skey_driver.driver.variables:
                        for v in skey_driver.driver.variables:
                            skey_driver.driver.variables.remove(v)
                    newVar = skey_driver.driver.variables.new()
                    newVar.name = "hide"
                    newVar.type = 'SINGLE_PROP'
                    newVar.targets[0].id_type = 'KEY'
                    newVar.targets[0].id = active_obj.data.shape_keys
                    newVar.targets[0].data_path = 'key_blocks["' + key.name.lstrip(obj.name.lower())+ '"].value'

import bpy

selected_obj = bpy.context.selected_objects
selected_obj.remove(bpy.context.active_object)

active_obj = bpy.context.active_object
shapekey_list_string = str(active_obj.data.shape_keys.key_blocks.keys()).lower()


for obj in selected_obj:
    for key in obj.data.shape_keys.key_blocks:
        if key.name.lower().lstrip(obj.name.lower()) in shapekey_list_string:
            if not key.name == "Basis":
                skey_driver = key.driver_add('value')
                skey_driver.driver.type = 'AVERAGE'
                if skey_driver.driver.variables:
                    for v in skey_driver.driver.variables:
                        skey_driver.driver.variables.remove(v)
                newVar = skey_driver.driver.variables.new()
                newVar.name = "value"
                newVar.type = 'SINGLE_PROP'
                newVar.targets[0].id_type = 'KEY'
                newVar.targets[0].id = active_obj.data.shape_keys
                newVar.targets[0].data_path = 'key_blocks["' + key.name.lstrip(obj.name.lower())+ '"].value'
                skey_driver.driver.type = 'AVERAGE'
                if skey_driver.driver.variables:
                    for v in skey_driver.driver.variables:
                        skey_driver.driver.variables.remove(v)
                newVar = skey_driver.driver.variables.new()
                newVar.name = "hide"
                newVar.type = 'SINGLE_PROP'
                newVar.targets[0].id_type = 'KEY'
                newVar.targets[0].id = active_obj.data.shape_keys
                newVar.targets[0].data_path = 'key_blocks["' + key.name.lstrip(obj.name.lower())+ '"].value'

Specifically, not knowing the formatting of this argument, or understanding how the key, key's owner, and data path were separately defined, was what made this solution take hours to find, despite many similar questions being available (though one was nearly working, I had to fix the formatting, so I consider this Q&A valuable in that it provides an updated answer.)

Specifically, not knowing the formatting of this argument, or understanding how the key, key's owner, and data path were separately defined, was what made this solution take hours to find, despite many similar questions being available.

original post used as basis for solution