The game doesn't end after you get the champion sword, you can still roam around, but after you turn in the sword, then the game ends.
You do not need to get the recipe to beat the game. You need the recipe to make the elixer of life, but if you find bottles of it in your travels and through treasure hunting, that is all you need. You only need the recipe so you can make a bottle, but you won't have to make it if you already have one. I found 3 or 4 elixers of life while playing.
I don't really want to give away spoilers, but it's used with something. So skipping this quest to the endgame is something you can do...
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