If you are starting in a new role, make it your first priority to talk to people who work close to you.
Your direct reports, their reports, your peers, those you will collaborate with in adjacent teams, your manager, their manager.
There is no rule for where you should stop, just do it with common sense.
And while the instict would probably push you to use the conversations to promote yourself, your background, your agenda, make it so instead that you will mainly listen. Understand who you are talking to, what motivates them, how they get measured, what success means to them.
If you do that effectively, you can’t fail. You will deliver exactly what they need, and they will be the ones promoting you and your agenda when that is needed.
Listening is the best self-promotion tool.