It is not currently known whether it's possible to use metallic hydrogen as a rocket fuel. However, if it is possible then the idea is simply to let the hydrogen turn into a gas. This isn't a chemical reaction, it's just a phase change like boiling water, so the waste product would just be hydrogen, likely in the form of a very hot plasma rather than $\mathrm{H}_2$. Combustion is a kind of chemical reaction, so this wouldn't be combustion.
Most phase changes would be completely useless as a rocket fuel. One could imagine filling a rocket up with ordinary compressed liquefied hydrogen and just heating it up and releasing the pressure to produce gas. This would produce thrust, but nowhere near as much as reacting it with oxygen, and it wouldn't be practical. However, metallic hydrogen is much more compressed than ordinary liquid hydrogen, and this causes the electrons not to be bound to the atoms any more. Because of this, letting metallic hydrogen turn into a gas (or a plasma) releases vastly more energy than letting liquid hydrogen turn into a gas - so much so that going on to then react it with oxygen wouldn't result in a meaningful gain in thrust.
The problem is that all that energy has to be put into the hydrogen when you compress it, so making metallic hydrogen is really really difficult. (The last time I checked, one lab had claimed to make a tiny amount, but it was controversial.) What we don't know is whether it's stable. That is, we don't know if it stays in the metallic state when you release the pressure, or if it just turns back into a gas immediately. If it's not stable then it's probably impossible to use it as a rocket fuel, because you'd need a really heavy tank to maintain the pressure.