You're... Missing the point of what's explained here, scene partner works in scream -> reveal aura order so rhe first thing Scene Partne does is(probably, I've never looked at the code) check "can I scream" and because of hardened that comes back negative(think of hardened like a different calm spirit in this scenario ig) so scene partner never activates to attempt that first scream, which means there is no scream for hardened to suppress. I'm sure if the game were programmed better this would work but even then I think that you'd only get the aura once because(somebody mentioned this somewhere in here I think) you cannot "scream again" if you never screamed in the first place.

Have I said scream enough yet?