Ask HN: Can I get some advice for a new manager resume?

I've managed a data science team now for about a year and I'm looking to explore new opportunities. My first step is to update my resume but I am struggling with how to talk about what I do as a leader. My first draft has a lot of "led this project", "orchestrated that effort", "managed this system". I do not think my resume is coming off as being detailed. How should I be talking about projects that I am in charge of, but I am not the one doing the day to day work on?

For any given project, I meet with the business stakeholder and strategize on the goal and solution. I break the project out into milestones. Then I hand those off to an IC on my team. I give feedback on their implementation. I help them with code issues as they come up. I regularly meet with our partners and give status updates and timelines. I help the IC refine presentation materials. Finally I coordinate with other teams to get the solution put in a production environment.

Im struggling with how to write a resume that makes me look like a good management candidate and I'd appreciate any advice.

Thank you