I sort of figured out how to do this by manually creating the menu button and appending it to outside of the “drawer”

var menuIcon = document.createElement("help-menu-icon");
        menuIcon.setAttribute("icon", "icons:help");
        menuIcon.setAttribute("label", "Help");
        menuIcon.setAttribute("link", "myurl.com");

        var link = document.createElement("a");
        link.setAttribute("href", "https://myurl.com");
        link.setAttribute("target", "_blank");

        menuIcon.appendChild(link);

        var icon = document.createElement("paper-icon-button");
        icon.setAttribute("id","button");
        icon.setAttribute("name","help");
        icon.setAttribute("tabindex", "0");
        icon.setAttribute("aria-disabled", "false")

        link.appendChild(icon);

        var toolTip = document.createElement("nuxeo-tooltip");
        toolTip.setAttribute("for","button");
        toolTip.setAttribute("position","right");
        toolTip.setAttribute("offset","0");
        toolTip.setAttribute("animation-delay","0");
        toolTip.setAttribute("label","Help");

        link.appendChild(toolTip);


        const app = document.querySelector('nuxeo-app');
        app.$.logo.appendChild(menuIcon);