Yes Medicaid does cover home health aides.
If you have Medicaid and need home health aides and home health care the Medicaid plan will pay for a home health aide or other home health care you need.
Also if you're a veteran and get veteran benefits then the VA will usually cover the cost of home health aides for the Veteran as well.
So if you're a Veteran or the person who needs care is a Veteran and gets VA benefits then ask the VA about coverage for home health aide and home health care.
They can also provide coverage for nursing facilities and usually have their own VA nursing facilities as well.
If you have regular health insurance then they may pay for some home health aide as well but not always.
Health insurance will sometimes also pay for some short term nursing home care as well.