Is the Fire Shield a damage-dealing spell for the purpose of the Imbued Wood Focus (Fernian Ash)?

Question

The Fire Shield spell (PHB, p. 242; emphasis mine) states:

[...] In addition, whenever a creature within 5 feet of you hits you with a melee attack, the shield erupts with flame. The attacker takes 2d8 fire damage from a warm shield, or 2d8 cold damage from a cold shield.

The Imbued Wood Focus (Fernian Ash) (ERLW, p. 277; WGE, p. 114; emphasis mine) states:

[...] When you cast a damage-dealing spell using this item as your spellcasting focus, you gain a +1 bonus to one fire damage roll of the spell.

Does that +1 fire damage applies the first time a Wizard does damage with his Fire Shield?

Answer 1

"Damage-dealing spell" is not a keyword in 5e, I can see two possible interpretations;

1. Fire Shield is a damage dealing spell as it can deal damage
2. Fire Shield is not a damage dealing spell as it does not deal damage directly but instead creates an effect that deals damage

It's up to your DM to make a ruling, there is no resolution from the official rules.

FWIW (nothing?) dndbeyond tags Fire Shield with the "Damage" tag.