What bond exists in "red oxygen", and can something similar happen with hydrogen?
That is what I found on wikipedia. It has a cubic structure and it was not predicted theoretically.
here the pressure is not very high but is high(10 GPa)
High-pressure studies of hydrogen typically employ a diamond anvil cell (DAC) made of two diamonds holding a few-micrometer-thick gasket containing a tiny sample of hydrogen.
These are some more images I could found of hydrogen at high pressures, but I do not think any of them are like red oxygen.

Sources

Bonding, structures, and band gap closure of hydrogen at high pressures

This is a must read: Solid Hydrogen at High Pressure