The VPN icon you are seeing could also be indicating that you have the Web Protection feature of Norton Mobile Security, NMS, enabled. This feature sets up an 'on device VPN' which is the only way that Norton can access the necessary Apple programming APIs to provide this feature. This feature has been known to interfere with internet connections.
If you are willing to try again, after installing and setting up NMS, could you send logs to Norton to help diagnose the issue? Test by turning off the Web Protection feature when you are blocked while using cell data.
Start by opening iOS settings on your device and scroll down to the bottom where the apps are listed. Tap on the Norton Security app and tap to Enable Debug Log.
Now use your device until it causes the issue you are having. Then shake your phone back and forth and a prompt will come up to send logs. Tap on Send Error Report and fill in any information requested. In your submission, please include "forum 'your username' " in the Case ID section of the report. Also include a link to this thread.
If you do send logs, please let me know and I'll notify my contacts to look for them.