My guess would be that the variable `$option` you're creating doesn't follow the guidelines you find in the Magento DevDoc.

Payload should be

 {
 "option": {
 "attribute_id": "141",
 "label": "Size",
 "position": 0,
 "is_use_default": true,
 "values": [ // -> this is an array
 {
 "value_index": 9 // -> this is an object within an array
 }
 ]
 }
 }

What you're creating is:

 $option = [
 "option" => [
 "attribute_id"=> "63",
 "label"=> "Size",
 "values"=> [ // -> this is an object
 [
 "value_index"=> 54164121323 //-> this is an object within an object
 ] 
 ]
 ],
 ];


What is the response you get from http://localhost/magentoTest5/rest/V1/configurable-products/747682908/options? 200?

EDIT:

Try this instead:

 $option = [
 "option" => [
 "attribute_id"=> "63",
 "label"=> "Size",
 "values"=> array(
 [
 "value_index"=> 54164121323 //-ìì
 ] 
 )
 ],
 ];