I don't think any EU One-stop-shop scheme covers "local" goods sales in other EU member states yet, i.e. an EU company has to register in all EU countries they

I don't think any EU One-stop-shop scheme covers "local" goods sales in other EU member states yet, i.e. an EU company has to register in all EU countries they hold stock in. That is changing with the Single VAT Registration (SVR) legislation, effective in 2028.