Adds a named SPFx web part to a SharePoint page - generic method which accepts parameters.

addCustomSPFxWebPartToPage.cs

private static void addCustomSPFxWebPartToPage(ClientContext siteContext, string wpName, string pageName, int wpOrder)
{
    // create page example..
    ClientSidePage page = new ClientSidePage(siteContext);

    // modify existing page example..
    //ClientSidePage page = ClientSidePage.Load(siteContext, pageName);

    // get the available web parts - this collection will include OOTB and custom SPFx web parts..
    var components = page.AvailableClientSideComponents();

    // add the named web part..
    var webPartToAdd = components.Where(wp => wp.ComponentType == 1 && wp.Name == wpName).FirstOrDefault();
    if (webPartToAdd != null)
    {
        ClientSideWebPart clientWp = new ClientSideWebPart(webPartToAdd) { Order = wpOrder };
        page.AddControl(clientWp);
    }

    // the save method creates the page if one doesn't exist with that name in this site..
    page.Save(pageName);
}