Is there a way to use the Project CSOM from a server side event receiver using an implicit identity?

I have a server side event receiver to handle publishing events, and I need to set a Project scoped enterprise custom field when a project is published.

I thought I would be able to use the Project CSOM to connect to Project Server to get this done. All of the examples I can find for using Project CSOM set the projectCtx.Credentials to a SharePointOnlineCredentials object.  I'm working on-prem, so I thought the code would be executed using the implicit identity of the user who triggered the event, the way that SharePoint event receivers work, so I never set the credentials.

It seems I was wrong about that, because I keep getting 403 - Forbidden errors when I try and do anything after creating the ProjectContext.

Is there a way to either create a credential object that the ProjectContext will accept out of stuff I have access to from within the event receiver (without a password), or tell the ProjectContext that it should use the identity of the user who triggered the event?

I can get the SPUser object of the user who triggered the event because the https://docs.microsoft.com/en-us/previous-versions/office/project-class/gg178241(v=office.15) passed in to the event receiver has the site ID and the user login name, so I could do something like

using (SPSite site = new SPSite(contextInfo.SiteGuid))
{
    SPUser user = site.RootWeb.SiteUsers[contextInfo.UserName];

    using (ProjectContext prjCtx = new ProjectContext(site.Url))
    {
        // can i do something with the SPUser object here?
    }
}

What can I do to to get the ProjectContext to work without requiring a password to make a credential object?