My iphone 8 shows that the wifi is connected but the is no icon at the top of the screen and won't connect with the internet.

Check your WiFi Router / Modem for --> Recommended settings for Wi-Fi routers and access points ...

Connecting to Wifi is first part and then getting connected to Internet is the second

1. If you are connected to a Wifi, doesn't necessarily mean you are connected to internet. If you are not connected to wifi could be a problem of iPhone settings or Router/Modem Settings
2. If you are not connected to internet is the sole issue of Router / Modem Settings. Contact you ISP immediately