What happens with Elemental Resonance and the generic part of a mana cost now? I'd say as you can't generate generic mana it adds the same amount of colourless to the mana pool, is this correct?

Yes, that is correct; nothing has changed here.

Elemental Resonance works with generic mana costs exactly the same way it always has: if it tries to add an amount of mana represented by a generic mana symbol to your mana pool, it adds that much colorless mana to your mana pool.