There is no core functionality to archive this in the backend.
If you have database read access to run raw queries you can use the following
queries to get an overview of all the categories that are linked to a certain product:
Option 1 => Get all categories of a product by entering the product's entity ID:
SELECT c3.sku, c2.value
FROM catalog_category_product c1
INNER JOIN catalog_category_entity_varchar c2 ON (c1.category_id = c2.entity_id)
INNER JOIN catalog_product_entity c3 ON (c1.product_id = c3.entity_id)
WHERE c2.attribute_id = (SELECT attribute_id FROM eav_attribute WHERE attribute_code = 'name' AND entity_type_id = 3)
AND c3.entity_id = FILL_IN_PRODUCT_ID_HERE
Option 2 => Get all categories of a product by entering the product's SKU:
SELECT c3.sku, c2.value
FROM catalog_category_product c1
INNER JOIN catalog_category_entity_varchar c2 ON (c1.category_id = c2.entity_id)
INNER JOIN catalog_product_entity c3 ON (c1.product_id = c3.entity_id)
WHERE c2.attribute_id = (SELECT attribute_id FROM eav_attribute WHERE attribute_code = 'name' AND entity_type_id = 3)
AND c3.sku = FILL_IN_PRODUCT_SKU_HERE
tree.expandAll()
in a browser console but unfortunately it will work only forManage Categories
page.