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It does download a fraction of a gigabyte per language pair; it does so on demand, so you only “pay” the storage for the languages you use.

It's possible with Neural Machine Translation models. Before being integrated into Firefox itself local translation was already available through the TranslateLocally add-on, see: https://browser.mt/

It has been possible for quite some time. I remember a few years ago, Google Translate offered a offline translation option (for a specific language pair) on my Android that required a couple hundred of MBs of download.