The hardest part is not always the task. It is remembering the task exists.
A new parent can be feeding a baby, recovering physically and still somehow be the person who knows whether there are clean muslins, what time the health visitor is coming and whether anyone has eaten lunch.
Support becomes much more useful when the planning is shared too.
Own a whole job
Instead of “tell me if you need washing done”, take responsibility for keeping the washing moving. Instead of waiting to be asked about dinner, decide how food is going to appear. If bottles or pump parts are being used, learn the routine rather than asking for instructions every time.
The exact division does not need to be equal every hour. The point is that one person should not have to manage both the baby and everybody else's task list.
Make rest possible, not theoretical
“You should sleep” is not especially useful if the baby is crying beside the bed and three people are about to visit.
Useful support might mean taking the baby after a feed, dealing with the door, putting a meal within reach, cancelling a visit, or creating twenty quiet minutes for a shower. Small protected windows count.
Be specific when you offer help
When somebody is exhausted, an open-ended question can become another decision. “I'll sort dinner and clean the kitchen. Do you want me to take the baby while you shower?” is easier to answer than “What do you want me to do?”
Do not turn feeding into one person's entire shift
Even when only one parent can do the actual feed, there are surrounding jobs: bringing water, changing the baby, settling afterwards, washing equipment where relevant, keeping track of supplies, and making sure the feeding parent gets food and rest.
Keep adjusting the arrangement
The first week at home is not a contract either. Feeding changes. Sleep changes. Recovery changes. Work starts again. A quick regular conversation about what is feeling heavy can prevent an arrangement that worked on day three from quietly becoming miserable by week six.