Unfortunately it is not possible to display dashboard items from an add-on for JIRA Cloud as macros in Confluence Cloud. In general, it is not currently possible to “install a single plugin that works for JIRA and Confluence”. At the very least, you will need to provide two atlassian-connect.json files, one for JIRA and one for Confluence. However, both of these could point to shared resources on your server.
It shouldn’t be surprising that you’re receiving 403 requests from the Confluence API…your add-on has not been installed in Confluence Cloud, so there is no shared secret between your add-on and that Confluence Cloud instance.