With the new Unearthed Arcana on Barbarians, if you are conscious but at 0 HP do hits still give you auto failed death saves?

Question

Beginning at 14th level, the divine power that fuels your rage allows you to shrug off fatal blows. While raging, having 0 hit points doesn’t knock you unconscious. You still must make death saving throws, and you suffer the normal effects of taking damage while at 0 hit points. However, if you would die due to failing death saving throws, you don’t die until your rage ends.

From the new barbarian Unearthed Arcana. Would the normal rule of being hit while at 0 hp give you automatic death saving throw failures even though you are conscious?

Answer 1

Automatically failing a death save doesn't depend on you being conscious or not, it depends on you having 0 HP.

Damage at 0 Hit Points. If you take any damage while you have 0 hit points, you suffer a death saving throw failure.

^{PHB, pg.197.}

And the Rage Beyond Death ability states:

you suffer the normal effects of taking damage while at 0 hit points.

Automatically failing a death saving throw is a normal effect of taking damage while at 0 hit points so yes, that rule still applies even though you are conscious.

Answer 2

you suffer the normal effects of taking damage while at 0 hit points

... is pretty clear. If the hit doesn't kill you from massive damage it is a failed death save, or 2 for a critical hit.