My teacher was Norwegian. And our English school books all included "to" or "past". We used British dictionaries, predominantly various editions of Oxford's English Dictionary. Probably one of the learner editions.

It's an odd enough thing that I didn't realize that anyone did this until maybe a year or two after moving to London in 2000, as most media as well tend to include the "past", and it's still common enough to include "past" that it didn't really register with me for a while that some people skipped it. It's hard to tell when I noticed, as I would always include "past" because I'd been taught to, and might very well have heard times without it and assumed implicitly the half was there without noticing it was omitted for the same reason....

The Danish definition is the opposite, and consisted with almost all other Germanic languages, and what's giving rise to this discussion. Norwegian has the same as almost every other Germanic language in that respect.

It's the English one that is out of step, and specifically modern English, as the Old English and Middle English examples follows the older Germanic use.

Compare Middle English "half thrid" with modern Norwegian "halv tre" which has the same meaning.

Searching Google Books, I came across "A Dictionary of the Scottish Language", John Jamieson (1846) that contains this:

"HALF, s. This term frequently occurs in a Scottish idiom, which affords mirth to our Southern neighbours. If you ask "what's o'clock," when it is half-past-three, a Scotsman replies "Half four", i.e. half an hour to four. "Ha!" says the Englishman, "then I must wait dinner a long while, for it is only two o'clock!" But this is a good Gothic idiom, yet common in Sweden; half fyra "half past three; half an hour after three;" Wideg.; literally "half four."

So apparently until at least the 1840's, Scotland held on to the Germanic way, while it seems likely it had fallen out of use in England given that the author expected it to be confused for "half of four" rather than "half past four".

So now I'm curious if this has changed meaning in Scotland since then too, and if so when. I'm assuming it must have, or I'd assume there'd be a greater awareness that this would cause confusion.

There seems to be very few uses of the modern English version in books, and the oldest unambiguous mention I've come across so far other than your example and the above dictionary (which uses it in the wider Germanic way) and a Scottish book from 1841, seems to be from 1997.

I've also found one from 1968 where I can't tell whether or not it uses the modern English or not, and whether or not it reflects genuine English usage or a mistake, as it's published in an American student publication (Generation, volumes 20-21, published by students at University of Michigan) and written in a broad English dialect that I can't tell for sure if is genuine or "adopted" by an American for the purposes of the story.

I'm sure there must be more, but it does seem like its more wider use is a a very recent thing - most mentions I can find are 2010 and later.

I've just sampled, but e.g. specifically searching for "half four" in in the 19th and 20th century gave me just a handful examples, while "half past four" gave me thousands. But of course that could mean it was just predominantly used orally. I've tried "half five", "half three", "half six" too and skimmed, with similar results, but not looked exhaustively. And of course this is Google Books - it's certainly not exhaustive.