Is dukkha conventional or ultimate? Is it different from the other two marks of existence?

There is no asymmetry because the word 'dukkha' in the context of the Three Characteristics (tri-lakkhana) does not mean 'suffering'; just as the word 'dukkha' in the context of feelings (vedana) does not mean 'suffering'. 'Dukkha' only means 'suffering' in the context of the Four Noble Truths.

'Dukkha' in the context of the Three Characteristics means 'unsatisfactoriness'; namely, the inability of impermanent (conditioned) things to bring permanent lasting true happiness. (Only the unconditioned Nibbana can bring true lasting happiness). Thus, the teachings state:

yadaniccaṃ taṃ dukkhaṃ, yaṃ dukkhaṃ tadanattā

That which is impermanent is unsatisfactory; that which is unsatisfactory is not-self.

SN 22.15

In the Pali, many words, such as 'dukkha', 'dhamma', 'nirodha' & 'sankhara' have different meanings in different contexts thus, in each different context, must be translated differently & appropriately.

The Buddha was fully enlightened thus perfectly coherent. There can be no contradictions in a Buddha's teachings. It is the famous translators & gurus who are misinterpreting the teachings.

In summary, as shown in the quotes below, only the ‘dukkha’ of attachment & egoism is real ‘suffering’ (mental torment/trauma). The ‘unsatisfactoriness' of conditioned things (dukkha lakkhana) and painful feelings (dukkha vedana) are not suffering (unless they are attached to).

Context 1 - Dukkha as suffering

In summary, (all) suffering is clinging to the five aggregates (as ‘I’, ‘me’ & ‘mine’).

1st noble truth

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‘I am’ is a construing. ‘I am this’ is a construing. ‘I shall be’ is a construing. ‘I shall not be’… is a construing. Construing is a disease, construing is a cancer, construing is an arrow. By going beyond all construing, he is said to be a sage at peace.

MN 140

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He is seized with the idea that ‘I am form’ or ‘Form is mine.’ As he is seized with these ideas, his form changes & alters, and he falls into sorrow, lamentation, pain, distress & despair over its change & alteration.

SN 22.1

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By & large, Kaccayana, this world is in bondage to attachments, clingings & biases. But one such as this does not get involved with or cling to these attachments, clingings, fixations of awareness, biases or obsessions; nor is he resolved on ‘my self.’ He has no uncertainty or doubt that just suffering, when arising, is arising; suffering, when passing away, is passing away.

SN 12.15

Contex 2 - Dukkha as pain

Here a bhikkhu is an arahant, one whose taints are destroyed, the holy life fulfilled, who has done what had to be done, laid down the burden, attained the goal, destroyed the fetters of being, completely released through final knowledge. However, his five sense faculties remain unimpaired, by which he still experiences what is agreeable and disagreeable and feels pleasure and pain. It is the extinction of attachment, hate, and delusion in him that is called the Nibbana-element …

Iti 44

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When the Blessed One had entered upon the rainy season, there arose in him a severe illness, and sharp and deadly pains came upon him. And the Blessed One endured them mindfully, clearly comprehending and unperturbed.

DN 16

Context 3 - Dukkha as unsatisfactoriness

“What do you think of this, O monks? Is form permanent or impermanent?”

“Impermanent, O Lord.”

“Now, that which is impermanent, is it unsatisfactory or satisfactory?”

“Unsatisfactory, O Lord.”

“Now, that which is impermanent, unsatisfactory, subject to change, is it proper to regard that as: ‘This is mine, this I am, this is my self’?”

“Indeed, not that, O Lord.”

SN 22.59

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Then, friend Yamaka, how would you answer if you are thus asked: A monk, a worthy one, with no more mental effluents: what is he on the break-up of the body, after death?

Thus asked, I would answer, ‘Form is impermanent… Feeling… Perception… Fabrications… Consciousness is impermanent. That which is impermanent is unsatisfactory. That which is unsatisfactory has ceased and gone to its end.

Very good, my friend Yamaka. Very good.

SN 22.85

Dukkha - contexts 3 & 1

All conditioned things are unsatisfactory — when one sees this with wisdom, one turns away from suffering. This is the path to purification.

Dhammapada 278

Contexts 1, 1 & 2, 1 & 1 and 1 & 3

Tisso imā āvuso dukkhatā, dukkhadukkhatā saṅkhāradukkhatā vipariṇāmadukkhatā.

There are these three kinds of suffering, my friend: suffering due to/about pain; suffering due to/of mental concocting; and suffering due to/about change.

SN 38.14

Note: That 'attachment is dukkha' is an ultimate truth because every experience of suffering is bound up in attachment.