Be careful about diving in and doing too much work yourself as a developer. If you do, sure, your team now has 11 engineers instead of 10. 10% bump!
What can you, as their manager, do to instead increase their productivity by 10%? Likely many things, and this is a lot more sustainable, because otherwise the team gets neglected from a manager support perspective while you're busy working with them.
Of course, find things to do technically to help the team if you want, that's a great idea. But don't assume that the best thing you can do for them is always to do what they are doing.
What can you, as their manager, do to instead increase their productivity by 10%? Likely many things, and this is a lot more sustainable, because otherwise the team gets neglected from a manager support perspective while you're busy working with them.
Of course, find things to do technically to help the team if you want, that's a great idea. But don't assume that the best thing you can do for them is always to do what they are doing.