Yes. I am of course aware that for more sectarian followers of Dzogchen this is a point of contention, and there are also disputes between different lineages about these terms. I am also aware that Krishnamurti’s language around awareness was fluid and changed over the course of his life - so that he began to make a distinction between awareness and attention for example (with attention being a state without any centre, implying that ordinary awareness still operates from a centre). But he was quite fluid about these terms in general, and choiceless awareness can very easily be understood to be synonymous with attention.
The Dzogchen approach with which I am more familiar is one where one is encouraged not to do anything in particular with one’s mental state, one’s state of mind. As with certain forms of Chan and Zen, ‘ordinary mind’, ordinary awareness is valued and left untouched, with the mind permitted to act spontaneously in whichever way it happens to, without being grasped at, attached to, or being condemnatory of its activities.
There are also distinctions in language and approach between the Mahamudra ‘style’ of open awareness and the Dzogchen ’style’ - with Mahamudra valuing more the noticing of thoughts as they arise, while Dzogchen emphasising the significance of the sky-like background of awareness itself. But these differences in emphasis do not interest me in particular.
Obviously, there are sectarian Dzogchen folk who want to limit the nature of open awareness to pure awareness without any objects - but this is mostly for reasons of dogma, because certain views about awareness (Rigpa) have become central to the tradition. Broken down by analysis, what these sectarian Dzogchen folk call ‘open awareness’ is in fact no different (in essence) from the classical Buddhist understanding of nirodha samapatti, the state of “cessation of perception, feelings and consciousness”. But in classical Buddhism this is only something that can be ‘experienced’ by a person who is completely empty of all thought, feeling, and self-consciousness (usually a Buddha). Even if sectarian Dzogchen folk believe this to have been a frequent occurrence within their own lineages (as believers usually do), it is still nevertheless somewhat of a rare event, and does not characterise the ordinary mind in a state of open awareness.
So I use the term more fluidly - as is done in wider culture (if you google ‘open awareness’ you will find most people using it in this way).
Don’t forget that there are sectarian Theravada Buddhists who continue to reject the characterisation of mindfulness as being present-centred and non-judgemental. This is because they have a narrow sectarian understanding of the Pali word Sati (meaning memory) - from which the Buddhist thinking around mindfulness arose - in which memory and ethical judgements play a key role. But this more conservative sectarian understanding of mindfulness does not interest me either.
Open awareness - like choiceless awareness - communicates to me a state of awareness that has no fixed border, that embraces and accepts any particular aspect of experience without judgement, like the sun shining in the sky filling it with light and warmth - even when the sky is full of clouds and weather. This is how I use the term.