Hissing means water movement. Period. It's a leak.
In valves, there are two kinds of leaks. Leaks external to the valve - i.e. puddles in places water does not belong. And leaks through the valve -- i.e. water flows in correct places, but the valve refuses to shut off all the way.
In a sink/tub, it's easy to recognize the second type -- the faucet keeps dripping. But it's hard in a toilet, because toilets stay wet, and there's nowhere to observe water movement.
We know for a fact that you have a leak; now it boils down to "where". A toilet has 2 valves: the huge valve that empties the tank into the bowl; and the refill/float valve that refills the bowl.
Pop off the tank lid. The tallest thing in there will be the fill/float valve. The second tallest will be a simple tube sticking out. It's like a "glory hole" for a reservoir; it's an emergency spillway in case the refill valve sticks open. Normally the water should be below that. If the water is overtopping the overflow valve, the leak is in the refill valve.
Otherwise most likely the leak is in the flapper valve; however you usually expect intermittent action of the refill valve in that case. The drain would be continuous, but the refill valve has some hysteresis/slop: it fills to point X and shuts off, but it won't reopen until the level falls somewhat. So it'd be off for 3 minutes, on for 15 seconds, repeat.
Refill valves and flapper valves are different items, but each is around $10US.