Ok so the
No such entity. error message comes from
This class is a custom exception class of Magento and it is used a lot in Magento 2.
Whenever you see code like:
catch (NoSuchEntityException $e)
This class is being used.
The problem in your case is that it's hard to find out from where that exception is being thrown.
So to narrow it a bit, you can start debugging the two classes related to your indexes that fail:
Magento\Catalog\Model\Indexer\Category\Product => catalog_category_product index
Magento\Catalog\Model\Indexer\Product\Category => catalog_product_category index
Fortunately, the second one extends the first one so you've got one starting point.
You've got to keep in mind that each of this indexer class uses action rows classes to process the reindexing:
To me that's where you should start debugging as those action row classes are the direct classes which are reindexing those two indexes.
I really hope it will help you find your problem.