Learn Farsi: او جیره‌بندی ذخایر را به عهده گرفت. - He took on the rationing of the reserves.

While به عهده کسی است describes a state (meaning it is the responsibility of someone), pairing به عهده with the verb گرفتن (to take) turns it into an action. The compound verb به عهده گرفتن means to take on or to assume responsibility for something.

Does the compound verb به عهده گرفتن take a direct object with را?

Yes, if the object is specific. Unlike the copula structure which describes whose responsibility a subject is, به عهده گرفتن is a transitive verb. The task being taken on is the direct object. Here, the specific object is the entire noun phrase جیره‌بندی ذخایر (the rationing of the reserves), so it must be followed by را.

I do not see the ezafe connecting عهده to a person here, like we see in به عهده او است. Why is it missing?

In this sentence, به عهده is locked into the compound verb به عهده گرفتن. Because the person taking responsibility is already the subject of the sentence (او), you do not need to link عهده to a pronoun with an ezafe. It functions purely as the fixed phrase for assuming responsibility.

I recognize ذخایر as reserves, but what is its singular form?

The singular is ذخیره (reserve or storage). is an Arabic broken plural, which Farsi frequently uses for formal Arabic loanwords. At this level, you will notice this specific broken plural pattern quite often, similar to how (island) becomes .