No network icon, even though network check mark is on

See the following Apple articles:

Connect to Wi-Fi on your iPhone, iPad, or iPod touch

Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support

If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network

If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support

Check the route settings -> Recommended settings for Wi-Fi routers and access points

Recommended settings for Wi-Fi routers and access points - Apple Support

If you need help with your Wi‑Fi password

If you need help with your Wi‑Fi password – Apple Support (UK)

•  You need to sign in to your router.
• The Wi-Fi network name, or SSID (service set identifier), is the name your network that has a password.

or If you have iOS 16 / iPadOS 16:

Go to -> Settings -> tap Wi-Fi -> tap on the hideen Password -> enter Passcode -> you will then see the Wi-Fi Password.

If they are On, turn Off Hotspot & VPN.