....Therefore, there is no net gain of energy here,.....
Wouldn’t that depend upon how you rated the energy use of the hydrogen + oxygen?
Are we talking about BTU’s ?
No, it doesn’t depend on how you measure the energy. In a reversible chemical reaction, like changing water to H and O, you can never get more energy out than was put in. It takes a certain amount of energy to break water into its components, and you get approximately the same energy back when you burn the hydrogen to produce water again.
As others have said, hydrogen is just a store of energy, not a source. It’s like a rechargeable battery: you have to put energy in to get energy out. There may be some situations where hydrogen is a more useful energy storage mechanism than, say, batteries, but they’re few and far between.
... unlike the “gas” stations that would be needed if you used hydrogen to fuel your vehicle. A car can transport far less energy as hydrogen than as gasoline, so a hydrogen-powered car will need to stop far more often for refueling.