Azure Active Directory (Azure AD) provides basic authentication services but lacks support for social logins or biometrics, making it less ideal for a business-to-consumer (B2C) scenario where diverse authentication methods and personalized experiences are crucial.

Microsoft Entra B2C stands out as the optimal solution for this scenario. It is specifically designed for B2C applications, offering support for multiple authentication methods including social logins and biometrics, enabling personalized user journeys, and ensuring compliance with data protection regulations. Its cost-effectiveness and scalability make it a perfect fit for the retail company's needs.

Azure Multi-Factor Authentication (MFA) enhances security through multiple verification forms but does not cater to the need for personalized user journeys or support social logins and biometrics, limiting its applicability in this context.

Azure API Management facilitates API management but does not provide the necessary authentication services or support for customized user experiences, making it unsuitable for the described requirements.