Hydrogen works just fine as turbine fuel, and does so in space launch turbopumps. Achieving full efficiency, power, and engine life on hydrogen will require tweaks to a pre-existing engine, of course.
On the environmental side, H2 normally burns hotter than hydrocarbons, which produces more N2O, but combustion temperatures can be regulated, and have to be to match turbine life specs.
Storage is the problem. All generators based on storing hydrogen in room-temperature liquids/solids share the problem of considerably worse net:tare ratios than liquid hydrogen tanks. LH2 adds cost and maintenance with cryogenics and still falls short of hydrocarbon energy density.
You can't get net energy by extracting H2 out of water, as that consumes all of the same energy that H2 produces in combustion, plus the losses. Energy cannot be created, only converted. For heat to be created to drive the engine, energy has to be lost elsewhere, in. In this case it's lost in joining two chemicals, which store potential energy (combustibility) in their state of separation.
If you had a different energy source (actually energy converter) on board, e.g. nuclear, you could use its output to propel the aircraft without the need for combustion.