Be the lighthouse.
There's something strange about running a construction project: The project manager is usually the person with the least actionable authority in the room. Aside from your own staff, none of the project leaders actually report to you. They all have their own contractual obligations of course, but they are certainly not there to do your bidding, and some of them (IOR, Building Manager, Client, etc.) may even take an adversarial position every now and then. Basically, they're all captains of their own ships, and they know how to sail them. What you have is whatever the contract grants you, and the charge to somehow get every one of those ships pointed in the same direction.
For a long time I thought the answer was to be the captain of it all. To grab the wheel of every ship and make whatever adjustments I felt needed to be made. That may seem like the easiest thing to do sometimes, but that's really just a fast way to exhaust yourself and annoy a lot of very capable people. It doesn't work, and it was never going to work. What finally clicked is that a good project leader isn't the captain of all the ships. Your job isn't to manage all of these individual teams, your job is to set the goal and find a way to help them get there with you. Get out of the water and be the lighthouse. You don't board someone else's boat and take the helm. You stand in one place, steady, and you throw enough light that the captains can see the rocks and steer around them themselves. They know how to do their jobs a lot better than you know how to do their jobs, believe me. What they don't know is what they can't see, your job is simply to clear the way, or help the teams navigate around whatever hazard you can't get rid of. Surface the issues, and pull everybody through it together. That part is yours, that's the light. Be steady, be focused, be fearless.
A leader makes people feel confident. A manager makes people feel anxious. Manage the project, lead the people. Be the lighthouse.