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.
The problem with those TV apps is DRM. All the major streaming services require that you either use a locked down platform (probably checking SafetyNet and more on Android TV) or settle for their browser UI which lacks dpad support and gets quality throttled to 1080p or lower.
Circumventing that DRM is possible, but no project at the scale of a platform like those would dare the both legal risk and support headache of making those circumventions (which are very liable to break) a core part of the OS.
Kodi (and distros using it like LibreELEC) exist for people who want a FOSS platform for using non DRM encumbered media with a TV remote interface.