This is documented; the second part matches first, so you need to define the 
group there. See :help /\@<=

I'm frankly surprised the three working examples you give actually work.

Interesting. The documentation doesn't specify with which engine (or both) 
referencing a group from inside the preceding atom shouldn't work. And :h \#= 
makes it sound like the new engine supports only a subset of what the old 
engine supports, so maybe my 3 working examples illustrate the real bug here? 
At the very least the discrepancy is confusing to somebody new to vim (ie me).

@Ben, you probably refer to this:

>   In the old regexp engine the part of the pattern after "\@<=" and
>   "\@<!" are checked for a match first, thus things like "\1" don't work
>   to reference \(\) inside the preceding atom.  It does work the other
>   way around:

However, this bug is with the default / new NFA-based regexp engine, which 
doesn't have this odd quirk:

>   However, the new regexp engine works differently [...]

In fact, by swapping the capturing group and reference and switching to the old 
engine, this then works. So, a clear indication of an inconsistency and bug.

Oh, I guess my documentation was out of date. Disregard my #2, then.

This issue still repros in 7.4.638 which has the updated documentation.

@ingo, yes, that's the help text I was referring to. I had missed the "however, 
the new regexp engine works differently..." text as you suspected.

However, I *don't* need to switch engines to see the pattern match, when I swap 
the capture group and reference. I *can't* get the unswapped pattern to match 
regardless of the regexpengine setting. So does the new engine have this quirk 
after all, in some situations?

@Ben, I see that as well (and don't understand why). Maybe the reduced example 
here is just bad; the original problem was more complex:

<div>Test div</div>More words
     ^^^^^^^^^^^^^^
This works works but leaves off the trailing >:

/\v%(\<(\w+)\>)@<=.*\<\/\1

So I'd expect this to work, but it captures nothing:

/\v%(\<(\w+)\>)@<=.*\<\/\1\>