NOTE: This is a last minute hack to just record the serial number at the time of invoicing. This will not grant the functionality of using serial nos. for that you need to maintain stocked items.
If you just need it when you’re creating an invoice, then simply customize Sales Invoice Item doctype and add a field for Serial No. For the new field, check In List View
Also change the print format a bit to include this.
For help, refer: https://erpnext.org/docs/user/manual/en/customize-erpnext/articles/child-table-
So your result looks like this now: