In 6.3.0, the devs explained in a patch note that skills like Ferocious Leap and Shield Assault gain shields as an "auxiliary effect" and so do not count as "shield abilities" for the purposes of the Shield Master CP. Hardened Armor follows the same pattern, i.e. it gains a shield for that morph which the base form and alternate morph do not have. Therefore the shield is an auxiliary effect, not a primary one, and Hardened Armor is likewise disqualified from benefiting from Shield Master.

The same thing applies to "Damage over Time abilities": Toxic Barrage, while it has a DoT component, does not count as a "DoT ability" because that DoT component is an "auxiliary effect" added by that one morph. The other morphs are purely direct damage, so Toxic Barrage is primarily direct as well, with an "auxiliary" DoT component.

The usage of "auxiliary" as "component added by only one morph" seems to be confirmed by the fact that Elf Bane extends the duration of Magma Armor and Magma Shell, which provide massive damage mitigation and a small Flame damage over time component. That Flame DoT exists in both the base form and the one morph (Corrosive changes it to a Poison DoT). It is not only tiny but also comes second in the tooltip, which might indicate it is not the "primary" function of the skill. Yet it counts enough to make Magma Armor/Shell qualify as a "Flame damage over time ability" for the purposes of Elf Bane.

Meanwhile, Cleave and both its morphs (Carve and Brawler) have a shield, yet they do not benefit from Shield Master. The shield is present in all three forms and gets an additional benefit from the Brawler morph. Yet none of that is enough to grant the skill the benefit of Shield Master.

There is something very inconsistent here.

If Elf Bane is properly extending Magma Armor/Shell, even though the Flame DoT does not seem to be the "primary" function of the skill, then is Cleave bugged in not having its cost reduced by Shield Master?

If Elf Bane is improperly extending Magma Armor/Shell, then please define "auxiliary" more clearly, since the examples you gave in the patch notes are not then adequate for us to be able to identify with any certainty what qualifies as a "primary" or "auxiliary" effect, which leaves us unable to identify what's working as intended and what's bugged.