The situation
A snack intended for people who have not eaten is offered.
English meaning: I've already had some, so I'm all right, thank you.
Read the Japanese original
もういただきましたので、私は大丈夫です。The questionHow should “I’m all right” be read here?
Read the explanation
Clues in the scene
I've already had some, so I'm all right, thank you.
The stated reason narrows “fine” to declining an additional snack.
Each choice explained
No additional food is needed for the speaker — Best fit
Already having eaten explains why no more food is needed, in a scene where snacks are being shared with others.
The speaker definitely wants two portions — Does not fit
Nothing asks for two portions or a larger amount. That turns a reason for declining into an extra order.
The ingredients were safety-tested — Does not fit
The speaker reports eating, not inspecting food safety. No such inspection or role is described.
Nobody should receive the snack — Does not fit
The answer concerns the speaker’s own portion. It does not tell the host to withhold food from everyone.
Same words, another scene
After hearing about the ingredients, a guest uses the same answer. The waiter was asking whether to replace the plate already served, not whether to add another portion.
The answer may now decline a replacement rather than an extra snack. The preceding offer determines what is being accepted or declined.
Do you mean the plate does not need replacing, rather than that you do not want another serving?
Literal meaning
The speaker says they are fine because they have already eaten.
What these words cannot tell us
Whether they want some other food, may eat later or how much they ate is not established.
A question to ask in real life
Then I will skip your extra portion and offer the food to those who have not eaten.