I will discuss mainly from the perspective of Theravada Buddhism.
OP: Now I am confused because I heard that somewhere in the Canon the
Buddha talked about the conciousness vinjana without boundaries that
the Arahat have.
What you're talking about is in MN 49 (and I think one or two other suttas).
Bhikkhu Sujato translated part of MN 49 as:
Consciousness that is invisible, infinite, radiant all round—that’s
what is not within the scope of experience based on earth, water,
fire, air, creatures, gods, the Creator, Brahmā, the gods of streaming
radiance, the gods replete with glory, the gods of abundant fruit, the
Overlord, and the all.
Viññāṇaṃ anidassanaṃ anantaṃ sabbato pabhaṃ, ...
This translation is problematic because there is no such thing as infinite consciousness in Buddhism. Equating Nibbana with infinite consciousness would be more of Advaita Vedanta rather than Buddhism.
In this answer, Bonn explained that this is a wrong translation. Although "viññāṇaṃ" is used, it doesn't always mean "consciousness". The grammatical form, used in this context, should be translated as "that which could be known" or "that which one could be consciously aware of".
The correct translation should be:
That which could be known (Nibbana),
is invisible, infinite, radiant all round—that’s
what is not within the scope of experience based on earth, water,
fire, air, creatures, gods, the Creator, Brahmā, the gods of streaming
radiance, the gods replete with glory, the gods of abundant fruit, the
Overlord, and the all.
Viññāṇaṃ anidassanaṃ anantaṃ sabbato pabhaṃ, ...
So, Nibbana is something knowable, but it is not within the normal scope of physical and mental experience. It is not even within the normal scope of the experience of gods. Nibbana is not a type of consciousness and is certainly not a self. Nibbana is also not a substratum or foundation for the cosmos, or for anything. Nibbana is not an Ultimate Reality of any kind. Rather, it's the highest bliss that is experienced when ignorance is uprooted and suffering is ended.
Now, with this translation, it fits perfectly with the rest of the teachings in the Sutta Pitaka.
In Iti 44, according to Thanissaro Bhikkhu's commentary here, the Buddha taught that for an Arahat, past physical death, all five aggregates are no longer operating. That includes consciousness.
OP: Is he talking about the knowing-being self that the Advaita is talking about? And what exactly is this consciousness that the Buddha
talks about: is it the same as knowing-being that Advaita talks about,
when the duality of self and not-self has been removed?
First, about Advaita Vedanta ...
In Advaita Vedanta, Brahman is the eternal Transcendental Ultimate Reality which is the foundation or substratum of the cosmos, while the Self (Atman) is the eternal, permanent core of one's being.
Atman and Brahman are identical in Advaita, while everything else is made out of Brahman like pots and pans made out of clay. It's only because of maya (illusion) that things appear to be different. It's also because of maya (illusion) that you see yourself as a limited being with a temporary identity (the ego), rather than being Atman and Brahman itself. This is how it is non-dual.
Advaitin gurus would suggest you to ask "Who am I?" and discover that the true "I" is Atman, which is Brahman. The Atman is also the Eternal Witness, or the Cosmic Consciousness, the "I" of every self-conscious being. After attaining Self-Realization (where the little ego-self drops away), one would remain existing forever as this one single Eternal Witness or Cosmic Consciousness, that witnesses through every self-conscious being and even witnesses directly without any beings.
According to the Hindu text Shvetashvatara Upanishad:
God, who is one only, is hidden in all beings.
He is all-pervading, and is the inner self of all creatures.
He presides over all actions, and all beings reside in Him.
He is the witness, and He is the Pure Consciousness
According to the Hindu text Bhagavad Gita 13.14:
Everywhere are His hands and legs, His eyes and faces, and He hears
everything. In this way the Supersoul exists.
What did the Buddha teach?
The self (atta) is the idea or thought that arises out of the inter-operation or inter-working of the five aggregates (form, feeling, perception, mental formations and consciousness). This is similar to how music is created when different parts of a musical instrument works together. See Lute Sutta. How the five aggregates work together is described by Dependent Origination.
Sabbe dhamma anatta means that all phenomena (including Nibbana), is not self. If you break a musical instrument into pieces, you won't be able to find music in any of the constituent parts. If you look at the five aggregates, you cannot find the self there. The Buddha means here that there is no eternal and permanent core of one's being, that is the self, not even Nibbana.
Rather, the self is an impermanent changing idea, that arises and passes away from moment to moment, depending on the operation of the five aggregates, just as other mentally generated ideas.
And what about consciousness? The Buddha taught the following, from MN 38:
"Just as fire is classified simply by whatever requisite condition in
dependence on which it burns — a fire that burns in dependence on wood
is classified simply as a wood-fire, a fire that burns in dependence
on wood-chips is classified simply as a wood-chip-fire; a fire that
burns in dependence on grass is classified simply as a grass-fire; a
fire that burns in dependence on cow-dung is classified simply as a
cow-dung-fire; a fire that burns in dependence on chaff is classified
simply as a chaff-fire; a fire that burns in dependence on rubbish is
classified simply as a rubbish-fire — in the same way, consciousness
is classified simply by the requisite condition in dependence on which
it arises. Consciousness that arises in dependence on the eye & forms
is classified simply as eye-consciousness. Consciousness that arises
in dependence on the ear & sounds is classified simply as
ear-consciousness. Consciousness that arises in dependence on the nose
& aromas is classified simply as nose-consciousness. Consciousness
that arises in dependence on the tongue & flavors is classified simply
as tongue-consciousness. Consciousness that arises in dependence on
the body & tactile sensations is classified simply as
body-consciousness. Consciousness that arises in dependence on the
intellect & ideas is classified simply as intellect-consciousness.
Think about it. How can the silent witness witness anything except through one of these media: eye, ear, nose, tongue, touch or mind? There was never a time, when there was consciousness being aware of something except through the eye, ear, nose, tongue, touch or mind. There is therefore no independent consciousness.
Consciousness is dependent on and conditioned upon these six media. It does not exist independently connecting all beings. The consciousness in every being may be of a similar type, but it's not the same consciousness.
For example, I can say that every candle has a similar flame, but it's not the exact same flame that appears on every candle. Each flame is different.
What is non-duality in Buddhism? Everyone has this duality of self and non-self. There's the "I" mental idea (the self), and the objectification and classification of perceived sensations into objects (in the mind) according to its relationship to the self. This is discussed in great detail in this answer. When one becomes enlightened, this duality which gives rise to suffering, will cease.
OP: I read somewhere that Buddhism says that knowing-being is not true: because consciousness always consciousness-of-something, in
other words it cannot be conscious-of-itself, and therefore
consciousness-of-itself or knowing-being as one thing is not possible.
The Buddha was very clear that there is no transcendental consciousness or transcendental core of being, that is aware of something beyond the six sense media.
From The All Sutta (also see this question):
"Monks, I will teach you the All. Listen & pay close attention. I will
speak."
"As you say, lord," the monks responded.
The Blessed One said, "What is the All? Simply the eye & forms, ear &
sounds, nose & aromas, tongue & flavors, body & tactile sensations,
intellect & ideas. This, monks, is called the All. Anyone who would
say, 'Repudiating this All, I will describe another,' if questioned on
what exactly might be the grounds for his statement, would be unable
to explain, and furthermore, would be put to grief. Why? Because it
lies beyond range.
Also useful is MN 38, in which the Buddha makes clear that it is not the SAME consciousness that wanders through one's life:
Then he went to the Blessed One and, on arrival, having bowed down to
him, sat to one side. As he was sitting there, the Blessed One said to
him, "Is it true, Sāti, that this pernicious view has arisen in you —
'As I understand the Dhamma taught by the Blessed One, it is just this
consciousness that runs and wanders on, not another'?"
"Exactly so, lord. As I understand the Dhamma taught by the Blessed
One, it is just this consciousness that runs and wanders on, not
another."
"Which consciousness, Sāti, is that?"
"This speaker, this knower, lord, that is sensitive here & there to
the ripening of good & evil actions."
"And to whom, worthless man, do you understand me to have taught the
Dhamma like that? Haven't I, in many ways, said of dependently
co-arisen consciousness, 'Apart from a requisite condition, there is
no coming-into-play of consciousness'? But you, through your own poor
grasp, not only slander us but also dig yourself up [by the root] and
produce much demerit for yourself. That will lead to your long-term
harm & suffering."