Health Savings Act of 2023 This bill modifies the requirements for health savings accounts (HSAs) to rename high deductible health plans as HSA-qualified health plans; allow spouses who have both attained age 55 to make catch-up contributions to the same HSA; make Medicare Part A (hospital insurance benefits) beneficiaries eligible to participate in an HSA; allow individuals eligible for hospital care or medical services under a program of the Indian Health Service or a tribal organization to participate in an HSA; allow members of a health care sharing ministry to participate in an HSA; allow individuals who receive primary care services in exchange for a fixed periodic fee or payment, or who receive health care benefits from an on-site medical clinic of an employer, to participate in an HSA; include amounts paid for prescription and over-the-counter medicines or drugs as qualified medical expenses for which distributions from an HSA or other tax-preferred savings accounts may be used; increase the limits on HSA contributions to match the sum of the annual deductible and out-of-pocket expenses permitted under a high deductible health plan; and allow HSA distributions to be used to purchase health insurance coverage. The bill also (1) exempts HSAs from creditor claims in bankruptcy, and (2) reauthorizes Medicaid health opportunity accounts. The bill allows a medical care tax deduction for (1) exercise equipment, physical fitness programs, and membership at a fitness facility; (2) nutritional and dietary supplements; and (3) periodic fees paid to a primary care physician and amounts paid for pre-paid primary care services.