Upon receiving the response, Turbo Drive replaces the whole <body> element and merges the contents of the <head> element. So it should use whatever title is present on the new response. Whether it changes or not depends if you are sending the same title in your response from the back-end.
If you reload the page after clicking the link, do you see your new title?
Also, the default visit action is advance (source), so you don’t have to specify it using the data-turbo-action attribute.