When you add your VAT ID to your account, your VAT ID will be displayed on your invoices going forward. You can also regenerate your invoices with your VAT ID by navigating to your Account page and selecting "Invoices" on the left-hand side and there will be 3 dots next to each invoice. If you click on the 3 dots next to the invoice you would like to update, there will be an option to update and regenerate the invoice.
Adding VAT ID shifts the liability of paying the taxes from Bubble to the user. Taxes aren’t added to the invoice and it’s the user’s responsibility to report the services bought from a non-EU supplier to their gov (e.g. by submitting Bubble invoices that display their VAT ID)