Do you have roaming enabled?
In order to stay in touch while traveling, you must enable roaming. You can find the roaming switch in the iPhone settings.
For some eSIM cards, you need to check the APN settings. APN configuration information is included in the eSIM card installation instructions that you received after purchase.
Do you have a signal?
If you find yourself in a place with a limited network coverage area or without access to a network, it will be difficult for you to access the Internet. Try changing your location and make sure you see enough signal bands to connect to 3G or 4G / LTE.
If you are in a cellular coverage area and have tried all the options, reboot the device and see if this solves the problem.