Hello Reconcad,
It looks like you're having some issues with the Wi-Fi icon on your device, even after you check in Settings > Wi-Fi and show the checkmark indicating it's connected. We know how important it is to be sure you're on the proper connection so you are not receiving an unnecessary charge on your cellular bill. You've come to the right place for help.
Let's start with making sure that your device is up to date, first making a backup of your device.
How to back up your iPhone, iPad, and iPod touch
Update your iPhone, iPad, or iPod touch
Do you currently have a VPN, security software, or private browsing/optimization app installed on your iPhone? If so, let's disable or remove the software and see if the icon appears again.
We hope this helps. Take care!