In Dependent Co-Arising, is Dukkha a Sankhara, a Vedana, both, or none?

It is because the world and our experiences are conditioned pain arises.

Verse 278: "All conditioned phenomena are dukkha"; when one sees this with Insight-wisdom, one becomes weary of dukkha (i.e., the khandhas). This is the Path to Purity.

Also, conditioned existence leads to one type of dukkha

• Dukkha-dukkha, the dukkha of painful experiences. This includes the physical and mental sufferings of birth, aging, illness, dying; distress from what is not desirable.
• Viparinama-dukkha, the dukkha of pleasant or happy experiences changing to unpleasant when the causes and conditions that produced the pleasant experiences cease.
• Sankhara-dukkha, the dukkha of conditioned experience. This includes "a basic unsatisfactoriness pervading all existence, all forms of life, because all forms of life are changing, impermanent and without any inner core or substance."[web 1] On this level, the term indicates a lack of satisfaction, a sense that things never measure up to our expectations or standards.

Dukkha

50 of the 52 cetasikas is Sankara

The Abhidhamma lists 52 kinds of cetasikas. One is feeling (vedanaa), another is perception (saññaa). The remaining 50 are grouped together under the term sa"nkhaaraa.

Here vedana is not Sankhara. But this leads to Dukkha.

• pleasant feeling is pleasant when it persists, painful when it changes;
• painful feeling is painful when it persists, pleasant when it changes;
• neutral feeling is pleasant when there is knowledge of it, painful when there is no knowledge of it.

Cūla Vedalla Sutta

So dukkha arises due to vedana and sankhara hence in this angle of thinking it is neither. Because of vedana and sankhara, dukkha arises hence in this angle it can be considered dukkha.

In D.O.,

• past and present sankhara is subjected to Sankhara-dukkha.
• whatever Vedana has an element of dukkha (pleasant feeling is painful when it changes; painful feeling is painful when it persists; neutral feeling is painful when there is no knowledge of it.)

Plenty of other things than vedana are dukkha, so you cannot say that dukkha is just vedana.

The buddha says that whatever is anicca is dukkha, so the way to find dukkha is to find something anicca, and all the stuff in Dependent Co-Arising are anicca.

the buddha says that this is to be known about dukkha:

"'Stress should be known. The cause by which stress comes into play should be known. The diversity in stress should be known. The result of stress should be known. The cessation of stress should be known. The path of practice for the cessation of stress should be known.' Thus it has been said. In reference to what was it said?

Birth is stress, aging is stress, death is stress; sorrow, lamentation, pain, distress, & despair are stress; association with the unbeloved is stress; separation from the loved is stress; not getting what is wanted is stress. In short, the five clinging-aggregates are stress.

"And what is the cause by which stress comes into play? Craving is the cause by which stress comes into play.

"And what is the diversity in stress? There is major stress & minor, slowly fading & quickly fading. This is called the diversity in stress.

"And what is the result of stress? There are some cases in which a person overcome with pain, his mind exhausted, grieves, mourns, laments, beats his breast, & becomes bewildered. Or one overcome with pain, his mind exhausted, comes to search outside, 'Who knows a way or two to stop this pain?' I tell you, monks, that stress results either in bewilderment or in search. This is called the result of stress.

"And what is the cessation of stress? From the cessation of craving is the cessation of stress; and just this noble eightfold path — right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration — is the path of practice leading to the cessation of stress.

"Now when a disciple of the noble ones discerns stress in this way, the cause by which stress comes into play in this way, the diversity of stress in this way, the result of stress in this way, the cessation of stress in this way, & the path of practice leading to the cessation of stress in this way, then he discerns this penetrative holy life as the cessation of stress.

"'Stress should be known. The cause by which stress comes into play... The diversity in stress... The result of stress... The cessation of stress... The path of practice for the cessation of stress should be known.' Thus it was said, and in reference to this was it said.

https://www.accesstoinsight.org/tipitaka/an/an06/an06.063.than.html

As usual dukkha arises from craving and ceases from the cessation from craving like that

“One who craves for and delights in bodily form, craves for and delights in dukkha. One who craves for and delights in dukkha will not attain liberation from dukkha. In the same way one who craves for and delights in feeling … perception … formations … consciousness, craves for and delights in dukkha. One who craves for and delights in dukkha will not attain liberation from dukkha.

https://suttacentral.net/sa7/en/analayo

If you want to find dukkha, just make craving arise and puthujjanas already crave and delight so it won't be hard to find dukkha.

So when there is no delight, this happens

"There are ideas cognizable via the intellect — agreeable, pleasing, charming, endearing, fostering desire, enticing. If a monk does not relish them, welcome them, or remain fastened to them, then in him — not relishing them, not welcoming them, not remaining fastened to them — there arises no delight. From the cessation of delight, I tell you, comes the cessation of suffering and stress. {By this means, Punna, you are not far from this doctrine and discipline."

At that time the Blessed One said to the monks: “You should rightly examine the eye as impermanent. One who examines it like this is called ‘with right view’. Because of rightly contemplating it, disenchantment arises. Because of the arising of disenchantment, one is free from delight and free from lust. Because of being free from delight and lust, I say the mind is rightly liberated.

“In the same way [one should rightly examine] the ear … the nose … the tongue … the body … the mind … [up to] … one is free from delight and free from lust. Monks, because of being free from delight and lust, I say the mind is rightly liberated.

https://suttacentral.net/sa188/en/analayo

And the way to not have delight is this:

“In the same way you should give right attention to feeling … perception … formations … consciousness, contemplating consciousness as impermanent, knowing it as it really is. Why is that? One who gives right attention to consciousness, who contemplates consciousness as impermanent and knows it as it really is, will eradicate desire and lust in regard to consciousness. One who eradicates desire and lust in regard to consciousness, I say, liberates the mind.

https://suttacentral.net/sa2/en/analayo

which is done with ''diligence''

“To a type of monks like this I say that they [should] cultivate diligence. Why is that? As such a monk trains in the faculties and delights the mind accordingly, is endowed with the necessities of life, and associates with good friends, he will soon attain the destruction of the influxes, the influx-free liberation of the mind and liberation by wisdom, knowing here and now for himself and realizing that: ‘Birth for me has been eradicated, the holy life has been established, what had to be done has been done, I myself know that there will be no receiving of any further existence.’

“Why is that? In relation to forms cognized by the eye which he could crave for with delight and become defiled by attachment, on having seen them that monk does not delight in them, does not praise them, is not defiled by them, and is not established in the bondage of attachment. As he does not delight in them, not praise them, is not defiled by them, and is not established in [the bondage of] attachment, he diligently progresses in the appeasing of body and mind.

“With the mind fully established in peace without forgetfulness, always concentrated and single-minded, with boundless joy in the Dharma, but still attaining the foremost concentrative attainment, he will certainly not regress by following a form with the eye. In relation to [sounds cognized by] the ear … [odours cognized by] the nose … [flavours cognized by] the tongue … [tangibles cognized by] the body … mind-objects cognized by the mind it is also like this.”

https://suttacentral.net/sa212/en/analayo