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Pretty sure for Cured/Pickled/Fermented stuff you need an expansion for your Konohana farm... the waterwheel I think? It comes with a fermenting pot... You can't make those items in your kitchen, I've never seen them sold in shops and it's never been a reward for a request.
So basically, you need a maker for those items. And in this game, it takes a WHILE to get the makers.