You should put your healthchecks
executables in /usr/local/bin or in /opt/bin. If you see your folder /opt is empty, means your linux distribution doesn't use it. So, the suitable place would be /usr/local.
/usr/local and /opt are where every "manual" package/program must be placed. /usr is for packages managed by package managers (i.e, dpkg). /opt is the "standard place" for manual packages according to FHS, but debian distros use /usr/local instead.
For configuration files, they must be placed on /usr/local/etc, since /etc is for configuration files of automatic packages and other system programs.
The correct place for your shared functions is then /usr/local/share (/usr/share is for shared files of automatic packages). Every file which is designed to be read-only and independent of the arquitecture belongs to /usr/share or /usr/local/share (if they are own by "automatic" or "manual" packages).
/usr/lib is for dynamic and static binary libraries (.so or .a), and not for "interpreted" libraries/functions.
Usually, interpreters have different subfolders in /etc/share/ for each version, and inside each version folder, different folders for scripts, locales, tests, samples and so on.
If some day you create an official repository for your package healthchecks
, you could migrate your /usr/local/healthchecks contents to /usr/healthchecks and /etc/healthchecks.