Havdalah blessings — are they considered a blessing adjacent to another?

Shalom u’vrachah.

The Rishonim disagree on this matter.

Rabbeinu Tam’s opinion is that they are a blessing adjacent to another; and the reason they all begin with “Baruch” is that they are short blessings. If they did not begin with “Baruch,” they would appear to be one long blessing.

The opinion of Tosafot is that they are not adjacent, since each one can be recited separately; and so it is written in the Jerusalem Talmud.

See the sources.

Tosafot, Pesachim 104b, s.v. “except for a blessing”
And Rabbeinu Tam says that “shehakol bara lichvodo” (“Who created everything for His glory”) and “yotzer ha’adam” (“Who forms man”) therefore begin with “Baruch” without a concluding formula, because they are short, like the blessings over fruits and mitzvot, and their opening is their conclusion. And with “asher yatzar et ha’adam” (“Who created man”), it must begin with “Baruch,” for if it did not begin that way, everything would appear to be one blessing. And regarding the blessing “la’asok bedivrei Torah” (“to engage in the words of Torah”) and “veha’arev na” (“and please make pleasant”), he says that it is one blessing, since “veha’arev na” does not begin with “Baruch.” And Havdalah, too, which begins with “Baruch” even though it is adjacent to the blessing over the light, does so in order that it not appear to be one blessing. However, in the Jerusalem Talmud it asks: But what about Havdalah? And it answers: Rabbi would separate them.