Internet doesn’t work on 5th gen iPad with iPadOS 13.4.1

Given your reported diagnostic efforts, it is possible that your Wifi router may be blocking access to internet resources for your iPad, or perhaps may have a problem with its DHCP Server function. A restart of the router might be helpful.

To restart your router, disconnect power from the router. Wait at least 30 seconds before reconnecting power to restart the router. When the router finishes its reboot (which may take several minutes), force-restart your iPad:

• On an iPad with a Home button: Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On an iPad with Face ID: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top button. When the Apple logo appears, release the button.

After restarting your iPad, verify your internet connectivity.

After the router restart, you may also need to restart other devices, to refresh their IP addresses, on your home network.

Respectfully, in summary, my understanding of your earlier statement is that your device works okay with other networks - and that other devices on your home network are working normally.

This, of itself, does not preclude the possibility of selective blocking by your router - or similar possibility of a device either having a duplicate IP address or an un-routable link-local IP address (due to a DHCP problem).

Reseting the device, or its network settings, will not necessarily be effective In resolving networking issues of this nature. The advice provided is designed to eliminate several potential causes of issues.

Without appropriate diagnostic steps, it is impossible to state that “the problem is definitely not the router...”.