Is there any ios app available on app store that could turn on cellular data automatically as soon as there is no connected WiFi and similarly disable the cellular data when known WiFi network is connected.
If possible, I'd try to run some tests over a week or two just to find out. If it does make a difference, it's never been anything that I can notice over a normal day.
All in your head. When WiFi is enabled and connected, cellular data chipset goes dormant. If you keep WiFi assist on then cellar chipset stays activated but still doesn't use much power because WiFi is in use. If you are noticing battery drain it's because you have low cellular service. Turn WiFi calling on and it will reduce battery usage wasted on searching for a stronger cellular signal.
You feel wrong.
There is no carrier data in the background when connected to wifi and if you turn off wifi assist that would be a definite no carrier data at all when on wifi. And no it will not drain the battery more. It's all in your head.