I’ve extended my license, but the app still shows this ‘Updates end in x days’ warning on the screen, even though it’s 3 years away.

That’s a bug. The latest maintenance release should have addressed this. What version are you running?
4.3.2
Even after restarting the app?
Yes, but not immediately. It shows up later.
Please send me a screenshot of the About panel via PM, thank you.