RAW, when using the Abjuration Wizard’s Projected Ward, who takes “any remaining damage”?


The Abjuration Wizard’s 2nd level ability Arcane Ward reads:

Starting at 2nd level, you can weave magic around yourself for protection. When you cast an abjuration spell of 1st level or higher, you can simultaneously use a strand of the spell’s magic to create a magical ward on yourself that lasts until you finish a long rest.

In the context of this ability, the wizard is the "warded creature", obviously.

The 6th level ability, Projected Ward, reads:

Starting at 6th level, when a creature that you can see within 30 feet of you takes damage, you can use your reaction to cause your Arcane Ward to absorb that damage. If this damage reduces the ward to 0 hit points, the warded creature takes any remaining damage.

To use Projected Ward, you must already have your Arcane Ward active, thus before using your reaction, you are definitely "the warded creature". In the description for Projected Ward, it says you are using "your ward", as in the ward that is warding you, to absorb the damage.

In the context of this ability who is the "warded creature", the wizard or the creature who took the damage that triggered the reaction?

The RAI seems obvious here, but I would prefer a RAW focused ruling.