Adding a bar code to an InDesign document from a CSV file

I want the CSV file to serve as my database, but I cannot update the CSV file because it has formulas (2) that "disappear" because the CSV file apparently only allows "values".

That is correct. Inside a CSV, all you're going to find are values:

item1,value1,value2,value3
item2,value4,value5,value6
item3,value7,value8,value9

If you have formulas in your spreadsheet, that means that you're working in Excel, or maybe Google Sheets? So you'd need your "database" to be a spreasheet in an application that can work with your formulas, from which you export a fresh CSV that can be your data source for data merge in InDesign.

If that won't work for you, you'd need to select a third-party tool if you wanted to use an Actual Database with InDesign. There are lots of such tools, usually in the category of "catalog plugins" like InCatalog or InData from Em Software, or maybe DataLinker from Teacup Software. These tools will let you connect database values directly to InDesign. There are many, many such tools, of varying scope and price, and you could let one of them help you automate your barcode-generation-and-data-merge workflow.