I just heard this mentioned on a Slack channel. WP Staging is a duplicator plugin that allows you to create a copy of your website. It creates a clone of your website into a subfolder of your main WordPress installation, including a copy of your database. And it does an entire search & replace of all serialised links and paths.
I am tempted to try it on a spare site just to see how well it works. As and when I do that I will report back here on how it went.