VAT number for Non-UK established seller

Hello everyone, hope you all are doing great.

I am an overseas seller and declared as Non-UK established business but LTD is registered in UK. Amazon acts as market facilitator for VAT collection and deducts 20% VAT on all of my sales. However, no VAT is deducted on amazon fee.

Question is: if I register for VAT and provide VAT number to Amazon, what will be the difference in VAT deduction. Is amazon going to deduct VAT on fee also.? and later I have to claim it form HMRC.? Please share your experience if someone has added the VAT number and saw VAT deduction in Fee also.

Reason of adding a VAT number is to get Auto receipt/invoice generation activated for business customers. As of now I send receipts manually within 24hrs of order dispatch.

Thank you