perf stat -p pid does not work with PMU events

Question

I am trying to use perf stat to measure the energy consumed by part of my code. To do that, I need to run my application first and once it reaches a certain point, I run perf stat, passing application's pid to it using -p flag. While this approach works for typical performance counters, it does not work with PMU events like power/energy-pkg/ or power/energy-ram. Does anyone know any workaround to capture the energy consumed by a block of the code?

Minimal, Reproducible Example:

$ cat example.c

#include <stdio.h>
#include <unistd.h>

int main()
{
    int pid= getpid();
    printf("my pid is %d\n", pid);
    sleep(15);
    return 0;
}

$ gcc example.c
$ sudo perf stat -e power/energy-pkg/ ./a.out   #(This works gracefully)

$ ./a.out &
$ pid=$!
$ sudo perf stat -e power/energy-pkg/ -p $pid      #(This doesn't work)

 Performance counter stats for process id '1749416':

   <not supported> Joules power/energy-pkg/                                           

PS: I already went through the following posts, but they didn't resolve my issues:

perf stat for part of program

Perf record after my code reaches a certain point?