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It is not, but it is considered burning.
It is not, but it is considered burning.
Technically incorrect.
"Burning" is fire damage over time, and Her Embrace does not itself cause you to do that. The only things Her Embrace causes are the ones listed in it's reminder text, none of which are fire damage over time. This is why (as /u/TheKurosawa mentions) it is not removed by things that remove sources of burning.
However the Oni-Goroshi item has a modifier that causes you to take fire damage over time while you have the "Her Embrace" buff. Because you can't gain that buff without having that item, you will always be burning while you have Her Embrace, but Oni-Goroshi's modifier is the source of the burning, not Her Embrace (this effectively "can't" be removed by the afformentioned burning-removal effects since you'd still have Her Embrace and thus begin burning again immediately, similar to why burning ground's effect isn't removed while you stay standing on it - imagine the complaints if burning removal effects caused you to drop the sword).
This also matters for e.g. how modifiers to the effects of buffs on you work (they don't make the burning more because it isn't an effect of the buff) but primarily is a consequence of fixing a communication issue that existed on The Goddess Unleased with the "Her Blessing" debuff. That was burning, which meant the fire damage over time it caused was an effect of the buff, and was thus listed in the reminder text for Her Blessing - which a bunch of players promptly didn't read assuming it was a generically positive effect, then complained when it killed them. Moving the damage to a property of the item makes it harder to miss.