Project manager
The person who knows who is waiting on whom. On a project with three or more people involved, this is the difference between two months and five.
When your project needs this person
On teams. With a single provider they take the role themselves, which is fine, as long as you know who you are talking to.
What happens when they are missing
The project stalls and nobody notices, because everyone is waiting on someone else. Usually it turns out everyone was waiting on you for something nobody told you about.
How this appears in an offer
Sometimes a separate line, sometimes inside the total. Both are normal. Ask who your point of contact is and that is enough.
What they do NOT do
Does not make business decisions for you and does not replace your approval.