Under what circumstances will a watchOS app not update automatically?

Thanks for the post. I would recommend to look at the watch sysdiagnose for the error first.

When a watchOS app doesn't update immediately after its corresponding iPhone app has been updated and remains stuck in the "Installing" status, several issues could be at play. Sometimes, the connection between the iPhone and Apple Watch can be temporarily unstable, preventing the watchOS app from updating correctly. Ensure that your Apple Watch has enough free storage space to install the update. Insufficient storage can cause installations to stall. The watchOS app installation requires a stable connection between the iPhone and Apple Watch, typically via Bluetooth. Ensure both devices are within range and connected to Wi-Fi if necessary. On your Apple Watch, go to Settings > General > Storage to check available space and delete unused apps or data if necessary. Verify that both devices are connected to Wi-Fi and that Bluetooth is enabled on your iPhone.

Hope this helps, however the sysdiagnose will be able to point the exact issue.

Albert Pascual
  Worldwide Developer Relations.