It depends on how things are run, but unless there’s a pre-decided consensus choice, multiple ballots would be likely.
And for this choice I’m not entirely sure it’s wrong for party leaders and elected officials to have a vote. It’s not like the Biden delegates were selected at random from the public to represent it in a momentous decision. No one thought the delegates would be anything other than a formality. They were likely selected as a reward for service to Biden or as a favor to some local official.