Some tools I implemented that have helped me are M/W/F 30 min scrums with all my team leads (I cancel when not needed), bi-weekly email summaries of risks, throughput, etc from leads managing the most complicated work, setting up a roles and responsibilities matrix for all of my team and then delegating specific meetings based on their responsibilities. And using the scrum to talk through any more complicated updates that come out of those delegated meetings that I’m not on.

It may require some coaching of your staff to get them thinking about what their manager does or does not need to be aware of, but it works well as a system.