Helly property for Artin groups

Determine which Artin groups are Helly, including whether the Artin group of type $A_2$ is Helly.

Background

Spherical-type and Garside groups provide broad families of Helly groups, but the notes leave the general Artin-group question unresolved and single out the type A2A_2 Artin group as a basic test case.

References

Which Artin groups are Helly? As a simple example, is the ${A}_2$ Artin group Helly?

— Group actions on injective spaces and Helly graphs  (2307.00414 - Haettel, 2023) in Section 14, “Open questions,” item 3