A person can be capable and still appreciate having one thing taken off their hands.

Competence is not the same as capacity to spare. Someone managing well is often managing a great deal, and the assumption that they have it covered means they are the last person anyone thinks to help, though a single item removed would change their week. Offering does not imply doubt about whether they could have done it.

Pick one person who visibly copes and take a specific job away from them. Collect the shopping, make the phone call, handle the booking. Say what you are taking rather than asking what they need, since deciding what to delegate is itself part of the load.