iOS 13.4.5 was recently renamed to iOS 13.5, due to an important SDK change for the COVID Exposure Notification API introduced in that update. Apple has just released tvOS 13.4.5 for the 4th and 5th generation Apple TV, and the HomePod.
tvOS 13.4.5 has no major features or noticeable changes, instead just performance and security fixes, as expected from a tvOS update. It can be downloaded by going to Settings > System > Software Update. It comes after Apple released Software Update 7.5 for the third-gen Apple TV just recently.
HomePod has also received the tvOS 13.4.5 update. It comes after Apple made the move from audioOS and iOS to tvOS update branding for the smart speaker.