The problem with Loco Translate for supported languages is that you are creating a custom translation. If you save the custom translation file in the normal location, it will be overwritten the next time WooCommerce updates the master Eesti translation file. If you save your custom translation file in the custom location, it will not be updated by WooCommerce and you will need to keep it updated yourself. This could be regular work. Neither options are good. The Loco documentation explains the normal location and the custom location.
Do you have a cache plugin, or are you using a content delivery service? It doesn’t look like you are from here. Its been a few days and, if caching were active, I would expect that the page would have been remade by now, but the phrase is still in English. I think caching should be disregarded as the issue.
I suggest a conflict test. Switch to the Storefront theme and deactivate all plugins except WooCommerce. It should work now. Then reactivate theme and plugins one by one and check to try to identify which software is changing the buttons, or preventing them from being changed.