iphone13 connection

If the Wi-Fi fan doesn’t appear there is no Wi-Fi connection, so that is a contradiction. There will always be a Wi-Fi fan if there is a connection.

As a first step, restart your router by unplugging for about 15 seconds (many routers do not have a true on-off switch).

Signal strength bars do not mean you have a cellular data connection, only that your phone connects to the mobile network and can make and receive phone calls. For cellular data you would have to turn that on in Settings/Cellular or using the Cellular Data icon in the Control Center.

An internet connection requires either cellular data on or a working Wi-Fi network connection.

Can you post a screen shot?

Do you have a Wi-Fi connection?

Do you see a Wi-Fi “fan” icon?

Do you see cellular signal strength bars?

Are you using VPN?