When I've been an engineering manager my policy has always been that I can work on code but only if that code is not on the critical path to shipping something my team is responsible for.

That's because management is an interruption-driven position. You just can't guarantee you can get 2-4 hours of productive, uninterrupted time.

Which means you shouldn't take on engineering responsibilities which, if delayed, will hurt your team.

So I'd still build stuff but it would be internal tools, or exploratory prototypes, or stuff that was absolutely not linked to any deadlines.

As far as I can tell coding agents have changed this quite a bit: I know a lot of engineering managers who are getting back into code now because they can carve out 30 minutes, and 30 minutes is now enough time to get something useful done.

I still think most managers should stay off the critical path to production though, at most organizations.