Same behavior here: The Team dropdown defaults to "None". I can drop down the text field and select my (Personal Team) account name, but when I do the box snaps back up, and a split second later my personal account reverts back to the word "None".

Suffering this same problem and spent about 24 hours visiting multiple solutions without success. I was pretty close on giving up, then decided to switch through various WiFi networks, seeing if using a fresh WiFi channel (and new bitrate) might unblock the update from happening. It seems to have worked! If you have an older watch like me, try connecting your phone via different WiFi standards. I use 802.11g by default on all of my devices, and temporarily switching to the slower, simpler 802.11b standard seems to have done the trick. Good luck.