Searching the whole DB for a whole word requires using --regex and
then using word boundaries. So to find pages that reference the TZ
environment variable, this *should* work (in principle):

  $ man -aK --regex '\<TZ\>'

It appears to work because it finds many pages. But it misses the
“tree” package (/usr/share/man/man1/tree.1.gz).

  $ zgrep 'TZ' /usr/share/man/man1/tree.1.gz
  \fBTZ\fP                Timezone for timefmt output, see \fBstrftime\fP(3).

As you can see, the nroff language intereferes with matching the
regular expression as “TZ” is surrounded by code. Users of man-db
obviously do not intend to have their regex matched against nroff
code. Thus operations are being performed in the wrong order. The
regular expression matching needs to happen on nroff-decoded text.

  $ zcat /usr/share/man/man1/tree.1.gz | nroff -man | grep '\<TZ\>'
       TZ        Timezone for timefmt output, see strftime(3).

* Workaround *

One approach:

  $ find /usr/share/man/ -iname \*gz -exec zcat {} + | nroff -man | grep '\<'"$whole_word"'\>'

In rare situations such as environment variable searches, case
sensitivity can be leveraged:

  $ man -aKI --regex TZ

In principle I certainly agree that this would be more usable, but I've
considered this in the past and given up as making it perform well would
have been very difficult.  There's a note about this in man(1), under
the description of -K:

              Note that this searches the sources of the manual pages, not the
              rendered text, and so may include false positives due to things
              like comments in source files, or false negatives due to things
              like hyphens being written as "\-" in source files.  Searching
              the rendered text would be much slower.