You... are not paying attentiont to the story, are you?
What do you think the thing they sign with blood at the batism is? Really, at least pay attentiont to what you are reading...
You think that just because they used blood, it must have been a contract? When Myne specifically says “Why do magic TOOLS like to use blood?”
Not to mention the fact that it’s explained that magic contracts use a special ink, and there’s no ink involved in the baptism at all.
Or the simplest fact of all: that they don’t actually sign a contract, which uses the blood of both parties involved to bind them to the
terms written on the contract parchment with the aforementioned ink. It’s a pretty big leap to conclude all that from the shiny coin that’s actually shown.
Really, at least pay attention to what you’re reading.
Also, by your logic (that “magic contracts use blood, so anything that uses blood must be a contract”): “steam engines need water to function just like humans do, so steam engines must be humans.”