Fog computing is emerging as geo-distributed and connected edge-to-cloud ecosystems, spanning multiple domains operated by different entities. Consequently, fog-compatible applications need to support distributed operations and decentralized management. This promoted the adoption of the microservices architecture, to facilitate application modularity and autonomy. Transitioning to fog-native applications, i.e., running distributed microservice workflows over multiple domains, is a challenging endeavor. On one hand, distributing workflows require awareness of the intents and dependencies of microservices, as this may impact the supply of data and the perceived Quality of Service (QoS). On the other hand, the variant capacities and energy supply, coupled with limited information-sharing across fog autonomies, hinders the prospect of end-to-end optimization. To tackle such problems, we propose a novel federate optimisation algorithm for multi-domain scheduling of fog-native microservice workflows. The algorithm incorporates workflow intents in decision-making by combining Bender's decomposition with Alternating Direction Method of Multipliers (ADMM) to provide optimized workflow placement, mapping, routing and admission. The performance of the algorithm is evaluated analytically and compared to state-of-the-art intent-based ADMM (iADMM). The results show performance trade-offs with the proposed iBADMM (direct), with the latter improving the fraction of workflow greenness by ≈ 15%.