Hello, I registered to try and help out.
I guess the checklist should be:
1) Make sure you have Pip-boy enabled, and then restart the game. (You said you did this).
2) Make sure your mobile devices is actually connected to wifi and isn't using mobile data. It must be connected to wifi.
3) Setup Firewalls.
When I ran Fallout 4 after enabling the pipboy app, it requested the following firewall settings in windows:
INBOUND RULE
-----
Name: Fallout 4
Group:
Profile: Private
Enabled: Yes
Action: Allow
Override: No
Program: C:\steam\steamapps\common\fallout 4\fallout4.exe
Local Address: Any
Remote Address: Any
Protocol: TCP (A separate rule was set for UDP with the other settings identical)
Local Port: Any
Remote Port: Any
Allowed Users: Any
Allowed Computers: Any
-----
When I get a chance to play again today, I'll try and use some tools to find out what port it's actually using. I wouldn't be surprised to see it using port 80 or 443 which is semi-standard for applications that don't want to bother with firewalls. In that case, make sure you're not running Skype in the background, as Skype is pretty notorious about interfering with those ports by default.
Good luck!