For example,
(?'int'[-+]?\d+)\h*b+\h*(?&int)
matches an integer with leading + or minus, some b characters, and then another integer (referenced with (?&int))

I won’t expound too much on this topic because it’s also in the documentation, but I’ve definitely written many over-long regexes that could have been hugely simplified by this method.

only mentions the two forms that work.

You are right. And I confirmed that’s been the case in Boost for the older versions used by N++ throughout my tenure on the User Manual… so apparently the section on named capture groups has always had that extra third group that shouldn’t’ve been there.

Interestingly, just because the Boost docs doesn’t list it doesn’t mean it’s not invisibly supported by that library: \g'name' or \k'name' as a backreference syntax aren’t mentioned, but it does work. But in this case, (?(name)...) is neither documented nor supported.

This is being fixed in PR#573

The first two work for me:
Search: (?<hi>world)
Replace: $+{hi}
and
Search: (?'hi'world)
Replace: $+{hi}

This fails with Invalid Regular Expression starting at the second (
Search: (?(hi)world)
Replace: $+{hi}

The Boost manual section in this only mentions the two forms that work.

As it says in the Searching > Regular Expressions > Substitutions section of the user manual

\<hi>

That is never a valid syntax. I assume you were trying for the “backreference” notation of \g<hi> or \k<hi>. But as the backreference user manual section says,

,

so even if you had used the right syntax for a backreference, it would not work in a replacement.