When metal type composition was still in use, a "block style"
blackboard bold font was available from Monotype. Much later,
this style (and I believe the identical shapes) was used in the
font charts from Unicode for the blackboard bold alphabet that
appears in the plane 1 block of "Mathematical alphanumerics"
(U+1D538-U+1D63B in https://unicode.org/charts/PDF/U1D400.pdf)
except for a few letters that had been defined previously in the "letterlike symbols" block
namely C, H, N, P, Q, R and Z).
The first public announcement of the AMS font containing a
blackboard bold alphabet appeared in TUGboat 6:2 (1985) in the article "Mathematical symbols and Cyrillic fonts ready for distribution" (https://tug.org/TUGboat/tb06-2/tb12beet.pdf).
A font chart of the egregiously misnamed
euym contains the alphabet (uppercase only).
A revised version of this article appeared in the next issue
(https://tug.org/TUGboat/tb06-3/tb13beetcyr.pdf), with the
euym fonts renamed to
msym and an explanation of why the
eu prefix was a bad choice. (The Euler fonts were designed by Hermann Zapf, who had no part in developing
msym. To even hint at such a possibility was an insult.)
The blackboard bold letters in
msym, although not shown in the revised announcement, are the same as those appearing in the first.
They are blocky in appearance, somewhat similar to those in the
Monotype blackboard bold, but of much lower quality. (It's no
surprise that Knuth did not like them.)
With the advent of Metafont84, the "extra symbols" fonts were
recreated, and a different style was used for the blackboard bold. As described in the quote that @Davislor has exhumed from
comp.text.tex, a different style was requested from the designer (whose identity is unknown to me), namely that the shapes and weights of the letters be compatible with Times bold, as AMS was intending to set their books and journals with a variant of Times.
(This was the font used on the Autologic APS-5; at that time, each typesetter manufacturer had their own proprietary version of most common fonts, since it was from fonts, not the equipment, that the manufacturers made their income.) At the time, this was considered novel, and although many authors are happy to use it, there are still strong feelings about what a blackboard bold font should ideally look like, as evidenced by the numerous packages on CTAN.
The announcement in TUGboat 10:3 (1989)
(http://tug.org/TUGboat/tb10-3/tb25ams.pdf -- thanks to @egreg for
finding this) appears to be the first mention that
available. No additional information is provided by the user's
guide for the
amsfonts package, version 2.2d (January 2002)
In my opinion, blackboard bold should blend with the principal fonts used in a document while remaining clearly distinct. Times does not really "match" Computer Modern, but neither does the Monotype style nor any of the various font packages posted on CTAN that I'm familiar with. Maybe it's time for a re-think.