Is it obligatory to make up or offer expiation for one who swallowed their saliva mixed with blood from a mouth wound while fasting, given the initial doubt about the presence of blood?

Swallowing normal saliva does not invalidate the fast. Doubt about the presence of blood mixed with saliva does not affect the validity of the fast, because the default is that the fast is valid and it is only invalidated with certainty. Expiation is only required for intentional sexual intercourse during the daytime in Ramadan.