My iPhone's Wi-Fi cuts off when I leave home

Wi-Fi has a limited range. If you move your device beyond the effective Wi-Fi coverage area, the signal will become weak and eventually disconnect. This is normal behavior and does not necessarily indicate a problem with the device or the Wi-Fi network.

Wi-Fi has a limited range. If you move your device beyond the effective Wi-Fi coverage area, the signal will become weak and eventually disconnect. This is normal behavior and does not necessarily indicate a problem with the device or the Wi-Fi network.

If you connect to Wifi, doesn't necessarily mean you are connected to the internet. --> Internet not available WiFi and Cellular … - Apple Community

Wi-Fi Assist is on by default. This will automatically switch to Cellular Data if the device is not connected to the internet.

About Wi-Fi Assist - Apple Support

When you are at home, what device provides your Internet Wi-Fi signal?

Did your Internet Service Provider supply you with a Wi-Fi router? What is the make and model number?