Mistakenly Recited 'Borei Pri Hagofen' Again After Havdalah

Greetings and blessings. In our Yeshiva, during Havdalah at the end of Shabbat, the one who made the Havdalah did not want to drink the cup of wine and therefore gave it to another to drink. However, by mistake, before he drank, he recited 'Borei Pri Hagofen' on the wine again. The question is whether the second blessing is an interruption since he had already fulfilled his obligation with the Havdalah blessing. I would appreciate it if the answer could be detailed so that we can publish it. (The answer does not have to be today) Thank you very much for everything.

Greetings,
He fulfilled his obligation with the Havdalah, and the blessing on the wine is not an interruption.

The Shulchan Aruch writes (Orach Chaim 271:15) that if one recited Kiddush, and before he tasted the wine, he spoke, he should recite 'Borei Pri Hagofen' again and does not need to recite Kiddush again. The same applies if the cup spilled before he tasted from it; he should bring another cup, recite 'Borei Pri Hagofen' on it, and does not need to recite Kiddush again.
It is clear that the blessing after Havdalah is not an interruption to the Havdalah blessing.
This is also clear from the Mishnah Berurah (ibid., subsection 78) in a similar case, 'But if beer or another beverage that was the local staple was found in that place, one does not need to take another cup for Kiddush but should recite 'Shehakol' on it and drink.'
There too, it is clear that the blessing one is obligated to recite after Havdalah is not an interruption to the Havdalah blessing.
The Mishnah Berurah says the same in the opposite case where one is obligated to recite the Kiddush blessing and not the blessing on wine. If one recited Kiddush on the cup thinking it was wine and it turned out to be vinegar or water, he should take another cup of wine, recite 'Borei Pri Hagofen' and recite Kiddush again because, since this was not wine, it turns out he did not recite Kiddush on the cup at all. However, if initially, at the time of the blessing, he intended to drink more wine, he does not need to recite 'Borei Pri Hagofen' again and only needs to recite the Kiddush. Again, the first Kiddush blessing, which was not properly made, is not an interruption to the 'Borei Pri Hagofen' blessing.
To explain the reason for this: it seems that since the blessing on wine and the Kiddush or Havdalah are all part of the order of the blessing, even though they were recited not according to this order, it is not an interruption.