Why does everybody (at least that I have ever seen), say "borei pri hagefen" first of all during havdallah, but not drink the wine until all of the other brachos have been said? Is saying the other brachos not a hefsek? How is the wine different from the spices, which I have always seen people smell immediately after making "borei minei bsamim"?
The reason being, that there are 2 types of Borei Pri Hagefen.
The first type is the classic one: You want to drink wine and you first have to make a Bracha. This is called ברכת הנהנין - a Bracha before enjoying something.
The second type is the "Shira" type. The Borei Pri Hagefen is the Bracha we use in that case - we then say other Brachot - and then somebody drinks some wine, if possible. It's more of a ברכת המצוות - a bracha said on the Mitzva at hand.
Examples are: Sheva Brachot, Brit Mila, Havdala and Kiddush.
Sources: שערי נישואין by ר' יהודה טשזנר, Ofakim 2009.
He's discussing whether the 7 Brachot can be said by 7 people, or whether you have to have the same person make the first 2 Brachot.
He brings the שו"ת להורות נתן in ח"ד אה"ע סי' ק"ה:
In essence, if you only say Borei Pri Hagefen wihtout some type if Shira, then you'd have to drink some of the wine. If you also say the secnod Bracha (of the 7 Brachot) then the Borei Pri Hagefen is a ברכת המצוות.
Anyway, we see from here that there is a concept of Borei Pri Hagefen that belongs to the next Bracha to form a Mitzva (Kidush, Havdala, etc.) and drinking the wine is secondary and waits until after the Mitzva is done.