The goal of an engineering manager is to make yourself unnecessary. If you're still essential after six months, you haven't done the job.

I've done engineering management for different teams, and the pattern is the same. You come in because something isn't working. The team is stuck, delivery is slow, people are frustrated. Your job isn't to fix it yourself. Your job is to instill habits. Talk about outcomes, lead by example, and be forgiving with the mistakes while being enthusiastic about the good steps. Success follows if the habits are good.

The real test is: does it hold after you leave? If the processes get dropped, if the one-on-ones stop, then you didn't instill habits. You were the habit. The team needs to understand why things work, not just follow instructions from the person in the room.