As was pointed out on that other question you linked, this is a surprisingly tricky sentence!
Let's slowly build it up.
It will take someone else.
What is "it"? Stopping Voldemort again. Implied but never directly said. As for "take", we could say "need" instead, just to be slightly clearer.
[Stopping Voldemort again] will [need] someone else.
This isn't "someone else" as in "we need a different person", but as in "we need other people prepared to do what you did, Harry". When will they be needed? "Next time" (that is, the next time that Voldemort tries to return).
[Stopping Voldemort again] will [need] someone else who is prepared to [do the same as Harry] next time.
Now, Dumbledore is saying that this someone else doesn't have to do much. Hence, it will "merely" (or "only") take someone else. This may sound like it's demeaning Harry's efforts, but it's meant to be reassuring Harry: standing up to Voldemort is not very difficult or unlikely after all, and it doesn't take someone extra-special to do it.
[Stopping Voldemort again] will merely [need] someone else who is prepared to [do the same as Harry] next time.
What, exactly, did Harry do that Dumbledore says they need other people to do (or be prepared to do)? "Fight a losing battle"--or what seems like a losing battle. (Dumbledore omits the word "like", but I'll leave it in for this one example.)
[Stopping Voldemort again] will merely [need] someone else who is prepared to fight a losing battle next time.
[Stopping Voldemort again] will merely [need] someone else who is prepared to fight what seems [like] a losing battle next time.
And now we just replace the bracketed bits with the different wording Dumbledore uses, and we have the sentence (okay, part of a sentence) that you bolded.
It will merely take someone else who is prepared to fight what seems a losing battle next time.
This is what was meant:
Yes, you are capable of sitting there. But you are not permitted to do so.
It's using the following senses of the words (from Merriam-Webster).
Can:
1 a : be physically or mentally able to
// He can lift 200 pounds.
May:
1 b : have permission to
// you may go now
Both can and may have multiple senses, and frequently can is used to express permission (rather than capability) in the sense of may quoted here.
So, the response from the guard, drawing a distinction between the two, is a kind of snide reply—inferring one sense of can to the person asking the question, rather than what would normally be assumed. No doubt the guard actually knew what the person was asking and just wanted to put them down subtly.
Best Answer
You have it reversed.
The first use of may admits a counter-argument before introducing a main point. The second use expresses a possibility. On the one hand, Harry only delayed his return (not fully defeated him), on the other hand it's possible he'll never return to power.
Notice that in the 2nd definition, the word may is "used when admitting...". May by itself isn't enough to create this meaning, it's only used as part of the idiom. The While here is simply another part of the construction that admits one thing before introducing another.