Depending on the size of your team and company, there's a good chance you'll be acting as both a people manager and a part-time individual contributor. When it comes to being both an individual contributor and a manager, which comes first? Should you prioritize management duties or shipping code?
The most effective managers operate in this dual role approach. Using sports parlance — part Player and part Coach. Taking this analogy further in the context of baseball, your job is to coach your team to win, but also operate as a utility player who can pinch hit when need be. You'll need to be able to turn double-plays when your second-base player is sick or on vacation.
I'd argue that you should actually always remain an individual contributor on some level — no matter the team size and even if it's just for small changes. It's important to stay in the trenches with the people you're managing so that you can lead them effectively and maintain their respect. Keeping yourself rooted in engineering best practices will allow you to empathize with the decisions your team makes as well as step into the game of shipping to production when your presence is needed.
One key to seamlessly alternating between Player and Coach is the type of work you take on as a Player. When I'm coaching, my job is help my team win and do the best work of their lives. When I'm playing, my job is to pick up the smaller pieces of work that are less desirable for whatever reason. This can mean fixing bugs, smaller maintenance tasks that are less fun to do or quick requests from the company that might derail the larger projects that require a focused flow state to really do well.
These tasks are more conducive to the segmented schedule that managers typically maintain because you can quickly jump into and out of the context without much effort. Reserve these frequent context switches for yourself so your team can focus on the longer term projects that need a state of flow to accomplish.
First and foremost, do whatever is necessary as Coach to enable the other people on your team to win. Then tackle the Player duties as your schedule allows it. Coach first, Player second.