My earlier solution worked only for a day, unfortunately. In addition to Apple Watch connectivity issues, I noticed sluggishness of the Peleton touch screen. What really fixed all my issues with Peleton+ including connectivity to Apple Watch was the Static Discharge procedure that I received from Peleton customer service. Here it is:
1. Power down your Bike's touchscreen by pressing and holding the power button. Skip to step 2 if unable to power down the touchscreen.
2. Unplug the power cord from the back of the Bike, and the two cords from the back of the touchscreen.
3. While the Bike is unplugged, press and hold the volume up and the power button at the same time for 30 seconds.
4. Keep the Bike unplugged for at least 1 full minute.
5. Plug the cords back in, and press and hold the power button until the screen illuminates.