tl;dr
October/November 1892
Deets
The Bengali original of "The Victory", জয় পরাজয় (jay paraajay, "Victory and Defeat") appears in the first volume of a multi-volume collection called গল্পগূচ্ছ (galpaguuchchha, "A Bouquet of Stories"). This volume was published in 1926. A Bengali calendar month and year are given at the end of the story: কার্তিক ১২৯৯ (kaartik 1299). That date corresponds to late October or early November 1892. Presumably this is the date of composition rather than of first publication.
Unfortunately, galpaguuchchha v.1 provides no bibliographic information about the original publication of jay paraajay or any of the other stories therein. It is unlikely that jay paraajay remained unpublished for 34 years. For one thing, as mentioned in the question, Jadunath Sarkar's translation of the story had appeared in 1911 with the title "Victorious in Defeat". Sarkar must have come across the Bengali original somewhere. Of course it's possible, albeit improbable, that Sarkar was working off Tagore's unpublished manuscript.
Subsequently, Tagore's own translation of the story, entitled "The Victory", appeared in a 1916 collection, The Hungry Stones and Other Stories. The preface states that "The Victory" was translated by Tagore himself. Further bibliographical information is not provided. As with galpaguuchchha, this collection too does not specify the first appearance of the original jay paraajay. Nor is there any indication whether this translation by Tagore had been previously published elsewhere. However, Pulinbihari Sen and Subhendusekhar Mukhopadhyay's far from definitive bibliography of English translations of Tagore's works, which appeared in a 1960/1961 volume of Indian Literature, does list this as the first appearance of Tagore's translation of the story.
Summary
- The Bengali original, jay paraajay, appears in a 1926 collection of Tagore's stories, and the date of composition given there is 1892
- The first known English translation, by Jadunath Sarkar, was published in volume 10 issue 6 of Modern Review, a Calcutta monthly, in December 1911, under the title "Victorious in Defeat"
- Tagore's own English translation, "The Victory", was most likely first published 1916 in The Hungry Stones and Other Stories.
Note
The Bengali script is romanized following iTrans conventions.