The exponential growth of Information and Communications Technologies (ICT) is projected to contribute significantly to global carbon emissions, necessitating energy-efficient solutions for sustainable network management. Network Function Virtualization (NFV) has emerged as a key enabler to reduce infrastructural cost, which, meanwhile, gains high potential to support energy-aware ICT with resource utilization and energy consumption optimization. However, standardization efforts lack comprehensive frameworks for carbon-aware orchestration, and energy measurement/coordination in multi-domain networks. This paper addresses this gap by first giving a comprehensive overview of current standardization efforts related to energy-aware ICT management from the perspective of 3GPP, ETSI, and ITU-T. Based on the gap analysis of current standardization, we present an architectural extension with new strata and functions, supporting decarbonization in NFV-based multi-domain ICT management. A case study applying this framework in a setting involving the orchestration of video surveillance services demonstrates the necessity and effectiveness of the functionalities in reducing energy consumption while maintaining service quality. Together with highlighting key challenges in the standardization of the proposed functionalities, this paper provides crucial insights into future standardization efforts, paving the way for a carbon-neutral ICT landscape.