After flushing, there is no water running back into tank to refill. What can I do besides adding water to the tank maually?

You may have problem with your fill valve or the angle valve.

Was it working before?

Have you checked the angle valve that it is fully open?

Have you done any work on the toilet tank?

See the images below and tel us which one is your fill valve,

My bet's on door #1. The FluidMaster.
This ballcock's has a history of the hole in the neoprene washer , (see image) swelling shutting off the water flow.
The solution would be to purchase a FluidMaster Replacement Seal # 243.
Shut the water off and twist the top off. Pop the seal out and replace it. Reassemble and you should be in good shape. Good luck, Tom

Check that the float bar is free and moves up and down. The bar usually a n arm with a ball float on it. Some toilets have a float that slides up and down, make sure that it moves freely. Both these devices turn the water on and off. You can also check that the valvue is fully open. You should haer water running.