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I don't see any issue with the Push-OutputBinding at my end. Whatever data I have received it is saving the same data in my Azure Data Lake Gen2 Container.
Downloading the blob file I can see the same data that I have written
Hello 在庫金額, This HTTP triggered function executed successfully.
I will suggest you to log the value of $APIResultsJSON on your function app to double check whether the data is converted before writing it to the Output binding.
There could be issue that the data would have converted when you have retrieve data from your API call. This will help you to figure out where exacting the data is converted.
...another idea: how did you define the file name in your blob storage? Is it problematic to call it xy.json?
regarding the encoding problem: https://www.weblogism.com/item/270/why-does-e-become-a