Coda Key Signature Question

My question derives from a piece of guitar music I was teaching. I came across what looked like a shocking ambiguity about the key signature in a Coda. Having typeset a simple representation in Dorico, I realised Dorico was doing the same…

Here’s the extract…

The issue for the player is whether the final C is sharp or not.

The player enters the Coda playing in 3 sharps. There are no sharps in the Coda. Is the C sharp or not?

In Dorico it’s not, but I can manually add a key signature (I might have hoped it would have added one itself). Or I can put a courtesy accidental in front of the final C.

My question, I suppose, is “Is what I’ve typeset actually allowable?” - Dorico thinks that C is natural, and that the final bar is in no sharps. But there is no courtesy “3 naturals” key signature at the start of the Coda. Is Dorico’s behaviour here slightly incorrect, or is it simply an artefact of the some arcane rule of typesetting that has the potential to confuse a player.

I’ll appreciate any comments you may care to offer on this “ambiguity”!

Dorico doesn’t currently take account repeats when it calculates key signatures, so it doesn’t take care of this kind of ambiguous situation automatically. We do plan to make Dorico able to sort out cautionary key and time signatures at repeat jumps in a future version (though not in the next major version).

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Thanks for your reply, and I appreciate that you also used the word ambiguity - it certainly made an interesting teaching point for my lesson when this cropped up in a book of guitar pieces…
Thanks again!