Rashi comments on verse 22 that the one goat, brought by each tribe, was to atone for the selling of Yoseif.

This explanation concerns me for a few reasons.

The 10 Martyrs were killed apparently because there had not yet been any atonement for the 10 brothers selling Yoseif.

And since each tribe brought the same offerings, including this one goat, why would the tribes of Ephraim and Menashe have brought goats, and Binyamin as well, since they had nothing to do with selling Yoseif?

I asked a rabbi about this first part, and he said that the case of the 10 Martyrs shows that these atonement goats did not result in a full atonement.

Searching through the various commentaries I could find, I do not see anyone asking more about this point. Ideally there might be a commentary which even shows in the text some hint that despite this goat being brought with the intention of being an atonement, that there is some indication that the offering was not fully accepted?

That is, does anyone here have any commentary on this goat in 7:22 (or perhaps 7:87 where they are tabulated in total) which either disputes with Rashi; or given Rashi, shows some support within the text for how to reconcile this Rashi with the explanation by the 10 Martyrs, that they were killed because there had not been anyone punished for selling Yoseif?

About Efraim and Menashe we can say that Yosef needs a Kaparah for the incident because he instigated the whole action (be Over on L'fnai Evair)

But we can say that there are two Dinim. There is a Gemarah in Kiddushin 40b (as paraphrased by Kollel Iyun Hadaf)

(i) (R. Elazar b'Rebbi Shimon): The world is judged by its majority, and individuals are judged by their majority.

1. By doing 1 Mitzvah, one can make himself a Tzadik, and change the judgment of the world to merit!

2. By doing 1 sin, one can make himself a Rasha, and change the judgment of the world to liability!
So not only what you do affects you but also others. The Kaparah here could be to protect the Klal against the lingering Aveira of the Shevatim (This would also answer why Menashe and Efraim needed to bring, since it would affect the whole Klal, including them.) But it never took care of the individual punishment for the Shevatim, thus you needed the 10 martyrs