I wonder if it is even possible to find a freelance request for proposals which is related to project management, a client seeking for a manager? Why is such a job so rare?
Usually you need a manager if you have many people in a project, so the ratio managers:developers is already low.
And then you have teams that have enough experience to manage themselves, means they don't need managers.
And then most people don't realize that they need a manager, just hire some developers, mostly unexperienced. When the project derails and they realize it, most of the time it is too late to get a manager on board or they don't realize how important it is, throw in more developers and go bankrupt even faster.
In the companies that realize how important managers are and that stay on the market as potential customers, usually there is already a manager or a team of them present, so they don't need a freelancer.
A good way might be to offer both management and consulting services, usually people are ready to pay for some consultation how to get the project running, and then you might have an in to convince them they need a project manager and that you would be a good fit.
If you charge differently for management and consulting, you should state this up front, not after you already have them convinced.