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It only says, "No network connection. Please try again later."
Nope
Did you make sure of your internet connection?
Yeah, it is connected to the internet but it could not connect the server.
I don't know if this going to work, but try the steps in this link on the app if possible and check if it will work: https://www.sony.co.uk/electronics/support/mobile-phones-tablets-mobile-phones/xperia-sp/articles/00...
I did these steps and it did not work.
Did you try to perform factory data reset?
When I try a factory reset, the phone's touchscreen not stop responding.
That's bad.
The thing is that the device is very old and it definitely reached end of support. So, what's happening with the phone is expected unfortunately. I don't believe that there's any troubleshooting steps that we can try further in this case.