I've seen plenty of managers who increased team output 10% for a few months by coding and completely lost the thread in the meantime. That's how your entire team gets laid off. Leadership doesn't care how much code your team writes, they care that you're working on the right stuff.
An engineering manager's job is: take long-term ownership for the performance of the team. That might include aligning with leadership, marketing your team's work internally, hiring, performance management, team bonding, planning, retros, oncall coverage etc. etc, although sometimes you'll have a PM/tech lead/HR contact who handle some of these.
Every now and then, your bottleneck really is just writing more code (more common in smaller companies). In that case, jump in.
An engineering manager's job is: take long-term ownership for the performance of the team. That might include aligning with leadership, marketing your team's work internally, hiring, performance management, team bonding, planning, retros, oncall coverage etc. etc, although sometimes you'll have a PM/tech lead/HR contact who handle some of these.
Every now and then, your bottleneck really is just writing more code (more common in smaller companies). In that case, jump in.