Does The List work for Ezreal's legend ability when exhausting it?

No, The List does not count toward Ezreal’s legend ability.

The Ruling

Ezreal’s legend ability requires that you have chosen enemy units and/or gear twice this turn with spells or unit abilities.

In Riftbound, there is a formal distinction between ability categories:

• Unit Abilities: Triggered or activated abilities originating from a unit (Rule 145).
• Gear Abilities: Triggered or activated abilities originating from gear (Rule 150).

Because Ezreal’s legend ability specifically limits the qualifying sources to "spells or unit abilities," an activated ability originating from a piece of gear does not contribute to the "chosen twice" requirement.

Why it does not work

1. Categorization: Per Rule 145 and Rule 150, the game treats unit abilities and gear abilities as distinct categories.
2. Specific Phrasing: Ezreal’s legend ability uses restrictive phrasing. In Riftbound, when a card specifies the source of an interaction (e.g., "unit abilities"), that restriction is authoritative.
3. No FAQ Override: There is no official Riftbound ruling or FAQ entry that classifies gear abilities as unit abilities.

Summary: Since The List functions as a gear card, its ability is classified as a gear ability. It does not meet the "unit ability" requirement specified in Ezreal’s legend ability text.

Note: I could not fully verify the classification of 'The List' against the retrieved rules.