It was working and suddenly stopped from one day to the other. I tested the module on other Odoo instance and it runs correctly, so the problem is somewhere in our settings, but I don't know how to debug such an issue, unfortunately my DB backups go back only one day I didn't think of keeping them longer.

check the settings you have changed over that day, also make sure that no newly added custom code or addons is not a reason for this

Is there a history? We are working more people on the same platform so I don't know for sure.

There is log for this i guess, if you have any old database backups just restore it in local and see what is missing

Correction, hope there is no logs by default, if you havent configured some custom module for this purpose, as per my knowledge

I have the latest code from branch 12.0 and I have a clean database with only Sales, Invoices, stock_picking_invoice_link apps installed and if I create a sale, deliver the products and create invoice, I don't see the Pickings on the invoice. If I go to the database and insert into the table "account_invoice_stock_picking_rel" the values (1,1) which is the invoice id and the picking id, then it will show the relation. To me it seems that it stopped inserting into that table.