My iPhone is simultaneously connected to both earphones and my watch. Why is the Essential News sound coming from the watch instead?

This is due to the compatibility limitations of the iOS system. When an iPhone is simultaneously connected to a Bluetooth headset and a smartwatch, the system will determine the audio output device based on the order of connection:
If you connect the headset first and then the watch, the voice of the news broadcast will be output from the watch.
If you connect the watch first and then the headset, the sound will be output from the headset.
It is recommended that when using voice functions such as news broadcasts, you adjust the connection order of the devices according to your needs to ensure that the sound is played from the device you expect.
 
Note: This feature is currently only available to overseas users.