Call REST API to get products, for example GET /rest/V1/products?searchCriteria[page_size]=3
Returned array should contain your added product with extension_attributes key inside
The extension_attributes is not present
In ProductRepository there is a line $this->extensionAttributesJoinProcessor->process($collection); which calls method responsible for extension_attributes, but despite that they are not included into product. If you request product details by calling GET /rest/V1/products/:sku the extension_attributes array is present.
It really makes no sense to call API once to get products, then call API to get configurable product details and then, finally, call API to get values and labels for configurable options. Is there easier way?