A patent application from the company spotted by Lowpass describes a system for displaying ads over any device connected over HDMI, a list that could include cable boxes, game consoles, DVD or Blu-ray players, PCs, or even other video streaming devices. Roku filed for the patent in August 2023 and it was published in November 2023, though it hasn't yet been granted.
The technology described would detect whether content was paused in multiple ways—if the video being displayed is static, if there's no audio being played, if a pause symbol is shown anywhere on screen, or if (on a TV with HDMI-CEC enabled) a pause signal has been received from some passthrough remote control. The system would analyze the paused image and use metadata "to identify one or more objects" in the video frame, transmit that identification information to a network, and receive and display a "relevant ad" over top of whatever the paused content is.
As long as the Amazon ones still come with Android, just throwing an APK of some FOSS media cwnter onto it is the cheapest way to get a reasonably modern "homebrew" appliance. The ads in the home screen are IMO a compromise I can deal with under that specific circumstances.