What is the correct printf specifier for printing pid_t

There's no such specifier. I think what you're doing (casting the pid_t to long and printing it with "%ld") is fine; you could use an even wider int type, but there's no implementation where pid_t is bigger than long and probably never will be.

With integer types lacking a matching format specifier as in the case of pid_t, yet with known sign-ness¹, cast to widest matching signed type and print.

If sign-ness is not known for other system type, cast to the widest unsigned type or alternate opinion

pid_t pid = foo();

// C99
#include <stdint.h>
printf("pid = %jd\n", (intmax_t) pid);

Or

// C99
#include <stdint.h>
#include <inttypes.h>
printf("pid = %" PRIdMAX "\n", (intmax_t) pid);

Or

// pre-C99
pid_t pid = foo();
printf("pid = %ld\n", (long) pid);

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¹ The pid_t data type is a signed integer type which is capable of representing a process ID.