Apple TV+ does not play content after age request on Mac

After updating to the latest version of macOS, the Apple TV app refuses to play age restricted content. I'm watching the Slow Horses show, and this is what happened when I tried to play the last episode of the 3rd season: I clicked the Play button, the app said that the content is for 16+, I clicked Continue, and then nothing happened. I try to click the Play button again, this time nothing happens at all - either I get an age confirmation dialogue, nor video playback. I'm 29 years old, almost 30, so the age should not be the problem. I tried to restart the app and Mac, clear app cache, check age restriction settings on the Mac, family sharing settings (I'm the admin), download the show, open it offline, without success.

I have two Macs both signed in with my Apple Account, the problem happens on both of them. The Apple TV app on my iPhone and iPad works as expected, it plays back the age restricted shows. Does anyone have any ideas what else can I do to resolve the problem?