Hydrogen is an indirect greenhouse gas with a Global Warming Potential(100) of around 11.6¹. Meaning it's over 11x worse than CO2 in the atmosphere! The main problem with this is that hydrogen molecules are extremely tiny, light and volatile, thus having a very high diffusivity. So unsurprisingly, hydrogen transport and storage has extremely high leakage rates. It's hard to alleviate because of the fundamental structure of the atom/molecules. Hydrogen can even permeate solid metals. A lot of the "green hydrogen" pitches don't take this into account.
And how much does it leak? If the amount leaking to the atmosphere is a thousand of the amount of CO2 that would have been released for the same process, it's still a huge net win.
Comparing the effect of one kg of H2 with one kg of CO2 is irrelevant if we don't know how much H2 is released compared to the amount of CO2 for corresponding processes to produce the same amount of goods.
Maybe this is a dumb question, but looking at GWP figures, it seems like there's nothing listed that's below CO2. Are there really no hypothetical gases to put in the air that is better than CO2 for global warming?
Some gases don't cause any warming at all. Helium for example is not a greenhouse gas. What you looked at probably ignored those, we generally only compare problematic ones that contribute to the greenhouse effect. CO2 has been chosen as the standard to compare everything else to, I'm not sure if there's any molecule that does cause some warming but has a lower 100-year potential than CO2. Interesting question, couldn't find an answer on the quick.
There are some zero or negative GWP gases actually, like water vapor which hovers around the zero point plus or minus epsilon, HFE 365mcf3 which is below 1, and obviously argon and nitrogen are at zero. Mostly people don't record GWP values that are below 1 since e.g. any common constituent of the atmosphere contributes negligibly.
It's remarkably hard to find organic compounds that are less-bad than CO2 though. It really is the very bottom of a local minimum.
H2 does not cause any warming at all, it's the reactions that do. So you're correct but that's exactly the problem. That's why I worded it as 'indirect' greenhouse gas.
¹https://www.nature.com/articles/s43247-023-00857-8