Is suchness, tathata, as a concept always something in addition to phenomena?

noun: qualia; plural noun: qualia

a quality or property as perceived or experienced by a person.

'Tathata' refers to how the laws of nature are the laws of nature, regardless of 'qualia'; regardless of if a Buddha arises to awaken to the laws of nature or not.

Ignorance is a condition for fabricators.

avijjāpaccayā, bhikkhave, saṅkhārā

Whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles, specific conditionality.

uppādā vā tathāgatānaṃ anuppādā vā tathāgatānaṃ, ṭhitāva sā dhātu dhammaṭṭhitatā dhammaniyāmatā idappaccayatā.

A Realized One understands this and comprehends it,

Taṃ tathāgato abhisambujjhati abhisameti.

then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it.

Abhisambujjhitvā abhisametvā ācikkhati deseti paññāpeti paṭṭhapeti vivarati vibhajati uttānīkaroti.

‘Look,’ he says,

‘Passathā’ti cāha:

‘Ignorance is a condition for fabricators.’

‘avijjāpaccayā, bhikkhave, saṅkhārā’.

So the fact that this is real, not unreal, not otherwise; the specific conditionality of it:

Iti kho, bhikkhave, yā tatra tathatā avitathatā anaññathatā idappaccayatā—

this is called dependent origination.

ayaṃ vuccati, bhikkhave, paṭiccasamuppādo

SN 12.20

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Now, observe that in the realization of impermanence there is the realization of many other things simultaneously. When impermanence is truly seen, this characteristic of impermanence is also the characteristic of dukkham, namely, it is ugly and unbearable. We will see the characteristic of not-self in it, also. Because these things are always changing, impermanent, unsatisfactory, and beyond our control, we realize anatta, also. Then we will see that they are void of selfhood, which is sunnata. We will see that they are just thus like that. Impermanence is just thus, just like that, thusness. And so, tathata is seen as well

Bhikkhu Buddhadasa

Is suchness, tathata, as a concept always something in addition to phenomena?

Perhaps it's the opposite -- i.e. phenomena without addition.

The suttas talk about craving and clinging -- from which I gather that you perceive things as "such" when you perceive them without adding craving and clinging etc.

Specifically, when Buddhists say phenomena are empty of own nature, do they always mean phenomena as such and not phenomena considered as themselves?

I have a feeling (given that you're using words like qualia) that you're assuming a knowledge of western philosophy or psychology which I don't have

I think that emptiness might be a doctrine which helps you to deconstruct what you construct when you perceive -- e.g. "that chariot is merely an assemblage of parts".

And as previously I think that suchness is what's left over, the chariot perceived without addition.

See for example what MN 11 says about "proliferation":

5. "Wanderers of other sects who ask thus may be answered in this way: 'How then, friends, is the goal one or many?' Answering rightly, the wanderers of other sects would answer thus: 'Friends, the goal is one, not many.'[2] — 'But, friends, is that goal for one affected by lust or free from lust?' Answering rightly, the wanderers of other sects would answer thus: 'Friends, that goal is for one free from lust, not for one affected by lust.' — 'But, friends, is that goal for one affected by hate or free from hate?' Answering rightly, they would answer: 'Friends, that goal is for one free from hate, not for one affected by hate.' — 'But, friends, is that goal for one affected by delusion or free from delusion?' Answering rightly, they would answer: 'Friends, that goal is for one free from delusion, not for one affected by delusion.' — 'But, friends, is that goal for one affected by craving or free from craving?' [65] Answering rightly, they would answer: 'Friends, that goal is for one free from craving, not for one affected by craving.' — 'But, friends, is that goal for one affected by clinging or free from clinging?' Answering rightly, they would answer: 'Friends, that goal is for one free from clinging, not for one affected by clinging.' — 'But, friends, is that goal for one who has vision or for one without vision?' Answering rightly, they would answer: 'Friends, that goal is for one with vision, not for one without vision.' — 'But, friends, is that goal for one who favors and opposes, or for one who does not favor and oppose?' Answering rightly, they would answer: 'Friends, that goal is for one who does not favor and oppose, not for one who favors and opposes.'[3] — 'But, friends is that goal for one who delights in and enjoys proliferation, or for one who does not delight in and enjoy proliferation?' Answering rightly, they would answer: 'Friends, that goal is for one who does not delight in and enjoy proliferation, not for one who delights in and enjoys proliferation.'[4]

Tathata is attitude you have when you really understand how and why things work the way they do.

For example, when kids are being kids, some people get angry. "Why are they noisy, why they don't listen, why they rush to judgement, why they are easily carried away?" etc. But when you understand kids, you know how they think, you know why this is a natural stage in development, you know how they grow and why it can't be skipped, you know what motivates them - then you don't get frustrated or as much as surprised, you can even manage them effectively. Your experience of kids and your attitude to them at that time is tathata.

Of course this is just a small example to illustrate the principle, but if you expand it to your entire life - you get the real Tathata.

Your question is an interesting philosophical investigation, if you can break or crack a concept, it will bring you closer to enlightenment, at least. In fact the Gōng'àn (Jap: Koan) is doing the same thing but in the Eastern style, more intuition, and 觀.

I do not think that I can answer you with a word or few sentences to define what is tathata, or suchness. In fact no one has ever been able to do so, else why we left fumbling it but the Buddha not defined it definitely like he did to the aggregates, karma... or paramita?

But perhaps I can help to unknot the knot in your question.

Is suchness, tathata, as a concept always something in addition to phenomena?

No. Parted from phenomena there is no tathata existed independently, parted from tathata neither phenomena. It's like, you cannot say the ocean or a droplet existed independently parted from the water, and vice versa.

Therefore you cannot say "something in addition to". Is the water in addition to the ocean that make the ocean an ocean?

If not, when we talk about the suchness of phenomena we could mean what they are like, the qualitative experience of a taste e.g..

I do not know where does this "suchness of phenomena" phrase come from? Perhaps reading some bad writings on Buddhism by Teacher XYZ? At least, in the Chinese text materials this phrase doesn't exist; this phrase construct is invalid and ludicrous.

In Chinese Buddhism, tathata is 如, or 如如. The Western civilization doesn't have equivalent concept, but I try to bring it closer for contemplation. The English words if, as it is, such as, as... could be close; or thisness/thatness the textbook one but really a bit misleading though. Hence, while your "the qualitative experience of a taste" is just an "as it is", "if", "as"; how more you can say about an "as it is" for giving the qualitative favor?

But if, conceptually, they are different, then no experience of taste amounts to its "true state" -- the meaning of suchness.

Again, you cannot put this 'no experience of taste amounts to its "true state"'; same as, is the true taste of the ocean the amount of all the taste of all the water, or just a drop of water? If it's the former, no existing being has ever known the taste of the ocean (perhaps it's sweet with caramel and orange tang? 😋)

Specifically, when Buddhists say phenomena are empty of own nature, do they always mean phenomena as such and not phenomena considered as themselves?

I can only say, tathata and svabhava are closely related but they are not the same.

Again, you cannot say "phenomena as such and not phenomena considered as themselves", simply phenomena, or anything, cannot have two contradictory qualia(s). You cannot say the rat is in the mammal class also the mammal class is excluding rat.

This last paragraph quoted is clouded with bubbling blurbs perhaps is unhelpful to understand the core teaching. Suggestion, drop it. Sometimes words and the mind's ability to construct syntax is a hindrance.

To answer your real concern,

I'm asking because I've seen it said that tathata means qualia.

This saying is an erroneous error. Tathata does NOT mean qualia. If it is that simple to define, why the Buddha has to spend another 20-30 years to teach the 2nd and 3rd Wheel Turning Sutras?