From the book Focusing in Clinical Practice, there are a number of different terms and descriptors for the statue of being in nonjudgemental presence with one’s own emotional state:
Ogden et al. connect this state with what is called “mindfulness of present-moment organization of experience.”
In Internal Family Systems Therapy (IFS)… the core concept is “Self,” which is a state of mind that has qualities of compassion, clarity, curiosity, and calm.
In Acceptance and Commitment Therapy (ACT), a similar concept is known as “self-as-context”:
Helene Brenner (2012) says: My first goal in therapy is to bring a stronger self, a stronger “I,” a stronger sense of self-efficacy, of self-autonomy, that there’s a strong “I” there. A self that is coming from a place of “I” and their own experience, rather than what everybody else tells them they should feel, rather than what they think they should feel or an externalized self.
[Still other concepts include] witnessing, observing, large, compassionate, spacious, content-free, and so on.
I, of course, have developed my own term for this, which I call present sense. It’s a derivation of the term present tense, which helps make it easier for me to remember. The core idea is to be in the present moment with your sensory input, not in the past, future and not in your thoughts.
I realized there is an analogy from computer science for this state, and that is the admin console. An admin console can see how particular computers or devices are operating without getting caught up in the operations themselves. That's essentially what this state is for people. The ability to step back, be with the current situation without getting caught up in it.