Besides improving the experience in case of session timeout; especially for users who are really intended to complete the process, maybe the possibility of the expiration and therefore the annoying need for re-authenticate should be eliminated or at least minimized. What do you think about letting the user know beforehand how much time they have until expiration, with a msg including a small timer? Something well balanced, not as obtrusive as an alert which causes panic, but still visible enough.
It could be shown after page load if it’s the starting point like in this case.
If instead countdown restarts after every activity(mouse click, keyboard etc), could be better to show the msg after some inactive time has elapsed. In that case there would be higher possibility that user doesn’t see it when it shows up, being at some other pages. So maybe an audio signal could be added.