Strengthening Community Care Act of 2023 This bill extends funding through FY2028 for the Community Health Center Fund (CHCF) and the National Health Service Corps (NHSC) Fund. The CHCF supports grants for outpatient health care facilities that provide care to medically underserved populations; the NHSC Fund supports the provision of scholarships and student loan repayment awards to health care providers who agree to work in areas with health care provider shortages.