Active participation is essential for collaboration to unfold its potential for learning, regardless of whether collaborative learning takes place in co-located, online or hybrid settings. Unbalanced participation remains a challenge in hybrid learning, with online participants contributing less than their co-located peers. In previous work, we addressed this issue by designing a sociotechnical hybrid collaboration setting aimed at promoting equal participation during hybrid collaborations. Promoting social interactions through a static collaboration script and one-time awareness-based collaborative reflection reduced the participation gap between co-located and online participants, but the observed effects were not statistically significant. This limitation highlighted the need for more adaptive support mechanisms. In this context, generative AI has emerged as a promising approach, offering real-time, context aware interventions aiming to promote participation. Based on data of hybrid collaborations, literature and expert interviews on the integration of generative AI in a sociotechnical hybrid collaboration setting, we developed four clusters of design recommendations (1) participation feedback, (2) individual participation prompts, (3) group participation prompts and (4) procedural guidance prompts. Central to these is generative AI-based assistance during collaboration to promote balanced participation. Three key functions of this recommended assistance are (1) real-time participation visualization based on live transcript analysis, (2) targeted inclusion prompts to encourage under-participating participants, and (3) adaptive collaboration scripting that respond to group dynamics. The proposed design recommendations aim to guide implementation of hybrid collaboration settings that make collaborative learning in hybrid settings more fruitful.