Hydrogen normally comes as a molecule (H2), not an atom.

Correct, but also just as importantly the He atom has both a higher nuclear charge and a full valence shell, which pulls the electrons in more tightly. I’d have to look it up but I believe a single He is even smaller than atomic hydrogen or at least comparable.

Edit: looked it up and yes, helium is smaller than atomic hydrogen.

Depends on your definition of smaller, but apparently it's not clear-cut: https://www.quora.com/Which-element-is-bigger-an-atom-of-hyd...