Man is calling Less; the only control at the man level is choosing which options to call Less with.
Less's search case-sensitivity is controlled by two options.
-I is in effect, then searches are case-insensitive: either
A can be used to match both
-i is in effect but not
-I, then searches are case-insensitive, but only if the pattern contains no uppercase letter.
If you make
-I a default option for Less, then all searches will be case-insensitive even in man pages.
Man-db passes extra options to the pager via the
LESS environment variable, which Less interprets in the same way as command line options. The setting is hard-coded at compile time and starts with
-i. (The value is
"-ix8RmPm%s$PM%s$" as of Man-db 2.6.2; the
P…$ part is the prompt string.)
If you don't want searches in man pages to be case-sensitive, or if you want them to be always case-insensitive, there is no way to configure this in man-db itself. You can make an alias for
man or a wrapper script that manipulates the
LESS enviroment variable, as Man-db prepends its content to the current value if present:
alias man='LESS="$LESS -I" man'
To turn off the
-i option and thus make searches always case-sensitive by default in man pages:
alias man='LESS="$LESS -+i" man'
You can also hard-code a different value for
LESS by setting the
MANLESS environment variable, but if you do that, then
man just sets
LESS to the value of
MANLESS, you lose the custom title line (“Manual page
foo(42)”) and other goodies (in particular, make sure to include
-R for bold and underline formatting).