You shouldn't need to rebuild it, but you will have to update any mySQL connections and server behaviors to mySQLi if you're using older versions that currently run on anything less than PHP5.2. It sounds as if your host is saying that you'll need to do that anyway as I suspect most shared hosting will only now offer PHP7x as a minimum. The good thing is that once you have the most recent version of DataBridge & mySQLi server behaviors installed, all you need to do is open the page, double-click on an existing server behavior and then click OK, and it will update.
Universal Email stopped being a standalone product quite a few years ago and is now part of DataBridge. Where are you seeing your Universal Email version number, as I can't see one even in the older files?