> These functions send a single datagram with the state string as payload to the socket referenced in the $NOTIFY_SOCKET environment variable.

The simplest implementation (pseudocode, no error handling, not guaranteed to compile), is something like:

    const char *addrstr = getenv("NOTIFY_SOCKET");
    if (addrstr) {
        int fd = socket(AF_UNIX, SOCK_DGRAM, 0);
        struct sockaddr_un addr = { .sun_family = AF_UNIX };
        strncpy(addr.sun_path, sizeof(addr.sun_path), addrstr);
        connect(fd, (struct sockaddr*) &addr);
        write(fd, "READY=1");
        close(fd);
    }