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Problem:
If you're experiencing an issue where adding an item to the cart in one language and then switching to another language allows the item to be added again, resulting in doubled quantities, this is due to the nature of WooCommerce's handling of stock levels across languages. This behavior occurs because the stock level isn't reduced to zero until the purchase is completed, similar to adding a product in one browser and then adding the same product in another browser.
Solution:
We recommend applying the 'Sold Individually' setting for your products. This setting prevents users from adding more than one of the same item to the cart, which should resolve the issue of duplicated items when switching languages. If you're using the Advanced Translation Editor, ensure that this setting is translated correctly. It might also be possible to synchronize this setting across translations automatically or through SQL updates.

If this solution does not apply to your case, or if it seems outdated, please check related known issues at https://wpml.org/known-issues/, verify the version of the permanent fix, and confirm that you have installed the latest versions of themes and plugins. If the issue persists, we highly recommend opening a new support ticket for further assistance.