There is a similar problem with any/bitset::any

Well, \indexlibrarymember{a}{b} adds "b under a" and "a under b" index entries, so the above is a natural fallout of this design. But I agree it's confusing in this particular case.

This seems somewhat ad-hoc to me. The general problem is that a single top-level index entry with subentries is used with multiple different meanings that differ across the subentries. Are there more such cases? Is the right answer to randomly select one meaning as the desired one and discard the others? Or should we maybe disambiguate the meaning and keep both entries, such as "set (m)" for the member and "set (t)" for the type or template?

Good point: Maybe we should just say "set (member)" for the bitset members to disambiguate (and assume a class / template) otherwise).

Maybe \indexlibrarymember should always replace a (\textit{member}). That may be generally useful information.

... at least for the first-level entry.

Your commit looks sensible, it's a nice local solution that's adequate for the problem.