Hyphens, En Dashes, Em Dashes

Q. This is going to throw some people, but here goes: I’m almost fifty, British school system education. We were taught that when an already hyphenated word appears at the end of a line, the hyphen should carry over into the new line:

After they were away for so long, their house

-warming party was a wonderful surprise.

Since the project I’m working on is British grammar, and yet I deal only with US people, this is a new one on them. Any input?

A. If this ever was British style (doubtful), it certainly isn’t now. If you can find an example in a published book or newspaper, do send it. Meanwhile, US style begins a line with a hyphen only rarely, such as for a broken URL.

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]