The puzzling thing is, if you check barcode table in version 13, there is a UOM field besides the barcodes, but it does not work.
UOM Field in Item Barcodes in your particular case was added by POSAwsome. Its not In V13 By default.
See here.
If you enable Show Barcode Field in Stock Transactions in stock transactions and scan a barcode on anything else It uses the Default Unit of Measure | Default Sales Unit of Measure | Default Purchase Unit of Measure Depending on the Document Type
Honestly the original PR [Enhancement] Multiple barcode per Item by GSLabIt · Pull Request #11917 · frappe/erpnext · GitHub seems really pointless without the UOM but according to the Original Feature Request it was meant to track supplier barcodes that differ from company barcodes. [FEATURE REQUEST]: Multiple barcode per Item not different UOM`s
From what I can tell, it should be simple to fix in all documents that can scan barcodes by modifying erpnext/erpnext/selling/page/point_of_sale/point_of_sale.py at 77e00403c82ea0d15caab65e81659dc10de73bed · frappe/erpnext · GitHub to return UOM along with the Item code and Using the UOM in erpnext/erpnext/public/js/controllers/transaction.js at de4450aee9a68eadf3d806003f42cd55bb4df804 · frappe/erpnext · GitHub