NORWICH—Registered nurses at the William W. Backus Hospital in Norwich, yesterday voted nearly unanimously to approve a settlement with the hospital, which followed a two-day strike. The agreement reached Saturday with Hartford HealthCare (HHC), which operates the 213-bed acute care facility, improves protective gear policies and empowers the caregivers to address staffing issues. The pact also resolves long-standing recruitment and retention concerns by making significant economic investments in the workforce.