Please take a look at this blog which talks about migrating your Tableau workbooks and data sources across project sites and servers- A Tableau champion's guide to migrating workbooks and data sources | Tableau Software. Hope this is helpful.
In 2019.3 with the Server Management Add-on Bundle, there is the Content Migration Tool that allows you to elegantly move Sites around. That just became available but requires 2019.3 or later.
Site Export and then Import is the way to go with the version you are on.