I think his penance is clearly meant to be Sisko not getting to retire on Bajor, and having to stay with the Prophets.
In S6E5 Favor the Bold, which is the first part of the two-parter that ends with S6E6, the episode where Sisko has the Prophets vanish the Domnion fleet, he speaks fondly to Admiral Ross about Bajor, and reveals that he plans to retire there. This is the first time Sisko indicates his fondness of Bajor has reached that point, where he wants to live the rest of his life there.
Note that S6E6 was also the conclusion of a Dominion War arc that covered the first 6 episodes of season 6. It started with the Federation leaving Deep Space 9 at the end of season 5, and ended with them returning.
Anyway, so in this arc we see Sisko fighting his way back to DS9 and Bajor, and in the penultimate episode of the arc there's an important development of his passion for Bajor. The arc then ends with him agreeing to pay an unknown penance to the Prophets. When discussing with the Prophets, their clue to his penance is:
The Sisko is of Bajor, but he will find no rest there. His pah will follow another path.
Between the arc's theme of Sisko fighting his way back to Bajor, him suddenly announcing his desire to retire on Bajor an episode prior, and the dialogue above, this is some pretty solid foreshadowing. Sisko's penance is that he would never retire to Bajor, that he would do something else, which we later learn is joining the Prophets. It wouldn't be for another 2 seasons until we see the fruits of this development, so it's understandable that there's some disagreement on the meaning of the penance. I know I didn't figure this out back when it originally aired.
It's also worth noting that we start to see the first hint of Sisko's half-Prophet lineage. While Sisko and the Prophets are arguing, they tell him they have every right to interfere in his life. This makes enough sense given the events of the series up until then, but upon learning that Sisko is literally a child of one of the Prophets adds another layer to this.
We see reinforcement of the idea that his penance means staying with the Prophets in S7E17 Penumbra, which is the first episode in the series-concluding 10-episode arc. In this episode, Sisko purchases some land on Bajor, and starts making plans for living there. Sisko and Kasidy are also making plans to marry. While Sisko is planning with a model house he made, the Prophet who inhabited his mother speaks to him:
SARAH: Your path is a difficult one. She can not share it with you.
SISKO: Are you talking about Kasidy?
SARAH: She cannot walk the same path.
This conversation is centrally about the marriage, however this also contributes to the idea that his penance is to join the Prophets. Not being able to stay with Kasidy is another facet of that.
Out of universe
As you mention, Memory Alpha also agrees with this interpretation. Since Deep Space 9 deals heavily in ideas of faith and prophecy, they avoided explicitly having any character just say 'the penance was this one specific thing'. However, in the Deep Space 9 Companion:
At the end of the episode, Sisko gets the Prophets to help him, but there is a price to pay; an idea with many mythic and biblical precursors. Hans Beimler says, "It's tragic hero stuff. A hero takes on things for others, but doesn't necessarily find any peace himself in the result." In relation to this, Ira Steven Behr compares Sisko to Moses (who guides his people to the Promised Land, but who isn't allowed to enter himself) and Ethan Edwards (the John Wayne character in the 1956 John Ford film The Searchers who reunites his family but cannot enter the house with them).
Which, while possibly an ex post facto rationalization, it certainly makes it clear that the penance is that Sisko himself could not have a happy ending.
The theory in the question indicating Jake being inhabited by a Pah-wraith is the penance does not jive with these pieces of foreshadowing, or the description from the DS9 Companion. Does the theory have some other pieces of evidence that back it up? Sisko does mention the then-unknown penance early in this episode, but he's merely wondering if the events of the episode (i.e. the titular Reckoning) constitute the penance, but that's not much evidence.
The other theory in the question that it involves the events of S6E26. I'm not sure I follow which elements of that episode meet the penance criteria. The Prophets going silent?
Since these are essentially temporary bumps in the road, they don't seem to meet the criteria of Sisko 'finding no rest [on Bajor]', or being a path that can't be walked with Kasidy.