How to deal with a sibling who has decided to take over all the decision making regarding the care of a parent or eldest single sibling?

My answer is, to support the person doing the caregiving.

If you are doing the caregiving, and being ordered around by a controlling person, choose: 1) Back them down, explain that you understand they have concerns and want to give their input, but there is a limit. 2) Allow them to do the caregiving if they are competent. 3) Is a person who is so controlling as to have the need to choose which market you shop really able to make good decisions for the person needing care?

Use boundaries. You are busy, and will talk to them another day.
Ask them to do something specific. Have them pick up groceries at their favorite market and deliver them, at their expense. Thank them for their support-fibbing if you must.

Unless you, as caregiver, are receiving some support by talking to a family member, talk to them less and less. imo.

I agree with Barb. If sibling thinks she can do it better, then she can take the caregiving on. This was a discussion I just had with my daughter. Turning the tables.

"Mom, if you are going to constantly tattle on me, then maybe you should go live with oldest sibling" It will give me a much needed break".

My feeling is always, "if you think you can do better, have at it".

We had a poster here named NeedsHelpWithMom. You can search her posts. Her mom lived with her for 15 years, mom stirred the pot with brothers who did nothing and refused daughter's requests to hire outside help. When daughter set some boundaries, mom called brothers to tattle. Daughter said, so go live with them!

Mom left, now has to pay caregivers because Brother and SIL aren't doing all that work. Daughter has her life back!

Beware of parents who play their kids against each other. I would take a giant step back from what you are providing.

Is there a POA?

No, sibling has decided after more than thirty years they can take better care of person needing help. I do not think it is a matter of taking financial advantage of person in need but more a matter of sibling feeling that know better than anyone else and considers themselves the favorite. It has gotten where sibling questions anything I do. Wants me to report to them on any and everthing. Doctors visits to choice of which grocerly store we go to. Seems like sibling wants to start giving orders on how we give care and wants to be in charge of our all of us live our live. Part of the problem is that person receiving care will complain to sibling when I do not something they think I should do.

"Decided" by what authority? Has this person been granted Power of Attorney or guardianship? Has the person who is in need of care been declared incompetent?