H and H- atomic and ionic radius
Electrostatic repulsion between electrons is the key to understanding $\ce{H-}$. The electrons might be delocalized, but they are also correlated - they avoid each other.

Both electrons of the hydrogen ion have the same energy level and they don't shield the charge of the core from one another.

The Aufbau and Pauli exclusion principles (and the assumption of hydrogenic orbitals) are insufficient to explain the structure and stability of $\ce{H-}$. In particular, it helps to drop the assumption that the electrons occupy the same spatial orbital and differ only according to their spin quantum number [1]:

As  pointed  out  in  the  introduction  Bethe  [5]  and Hylleraas [6] were the first authors to prove the stability of the negative hydrogen.  But it was Chandrasekhar [1]who first introduced a clever wave function to describe the H− system which leads to a beautiful physical picture. The key concept introduced by Chandrasekhar was to break the symmetry between the two electrons, which is a way to introduce implicitly the electron correlation.  [...]
We conclude that the negative hydrogen ion is a special  atomic  system  whose  stability  depends  completely on the electron correlation. [...] mean field theories and other approximations do not take into account correlation, preventing the possibility of predicting stability for the negative hydrogen ion.

Reference
[1]. Ignacio  Lopez  de  Arbina  de  Frutos. Stability of the Negative Hydrogen Ion:  Variational Approach with Electron Correlation.