The kapoteh is a long black frock coat worn by some Lithuanian Jews and Chabad Chassidim. It is very similar to a bekishe.
I was wondering what age do most Chabad Chassidim start wearing the kapoteh. From bar mitzvah?
From the wedding day onward.
Discussed in the book Mazal Tov by Rabbi Nissan Dovid Dubov on page 64 169. After the Kabbolas Ponim the chosson prepares for the chuppah in the following way. 170. The custom is that the chosson should wear a kittel. The Kittel is worn over a silk kapote but under a coat.
footnotes: the chosson doesn't wear the kittel the first yom kipur after after marriage. sefer haminhagim page 67. likkutei levi yitzchock igros kodesh p. 206 and also isru chag sukkos 5711 talks about the importance of wearing silk kappotes on shabbos and yontiff. from the Rebbe Rashab in sefer hamaamarim 5662 p. 231 and 247 talks about the importance of a silk garment on shabbos. also sefer hamamaarim 5673 page 328 (247), and sefer hamamaarim 5672 vol 2 p 872
From my personal observation though it seems like most chassanim put the kapote on before kabbolas ponim for the sake of convenience as that is when there are pictures being taken and the kittel and extra coat being put on right before the chuppah.
Another note: kapote, sirtuk, and bekishe are interchangeable names. There are many styles among these types of coats.