bluetooth: CTS: Fix includes to avoid build error with some libCs

Remove unnecessary include in header and source file.

gmtime_r() is an extension to the C library, and therefore one
needs to explicitly ask for its prototype to have it exposed.
This is done by defining _POSIX_C_SOURCE so let's do so.

These two changes fix build errors with some libCs.
Tested with pico, newlib, minimal and the host glibc.

Signed-off-by: Alberto Escolar Piedras <alberto.escolar.piedras@nordicsemi.no>
(cherry picked from commit a785548d)