This is a solution I was thinking about as a solution for EU contractors actually. Since Upwork is an intermediary, why not billing Upwork. You don't actually need to send the invoice to Upwork, but you can edit one for your accounting.
Concerning the VAT exemption, there it doesn't influence your invoice. You just don't add VAT. You may need to reference the tax code section which exempts you from VAT on the invoice however.
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