You almost had it, except that you need to use the lower-level curses function setupterm instead of initscr. setupterm just performs enough initialization to read terminfo data, and if you pass in a pointer to an error result value (the last argument) it will return an error value instead of emitting error messages and exiting (the default behavior for initscr).
#include <stdlib.h>
#include <curses.h>
int main(void) {
char *term = getenv("TERM");
int erret = 0;
if (setupterm(NULL, 1, &erret) == ERR) {
char *errmsg = "unknown error";
switch (erret) {
case 1: errmsg = "terminal is hardcopy, cannot be used for curses applications"; break;
case 0: errmsg = "terminal could not be found, or not enough information for curses applications"; break;
case -1: errmsg = "terminfo entry could not be found"; break;
}
printf("Color support for terminal \"%s\" unknown (error %d: %s).\n", term, erret, errmsg);
exit(1);
}
bool colors = has_colors();
printf("Terminal \"%s\" %s colors.\n", term, colors ? "has" : "does not have");
return 0;
}
Additional information about using setupterm is available in the curs_terminfo(3X) man page (x-man-page://3x/curs_terminfo) and Writing Programs with NCURSES.