Read "/proc" to know if a process has opened a port

I can read the /proc/$PID/net/tcp file for example and get information about TCP ports opened by the process.

That file is not a list of tcp ports opened by the process. It is a list of all open tcp ports in the current network namespace, and for processes running in the same network namespace is identical to the contents of /proc/net/tcp.

To find ports opened by your process, you would need to get a list of socket descriptors from /proc/<pid>/fd, and then match those descriptors to the inode field of /proc/net/tcp.

Please

cat /proc/$PID/net/tcp

and you will get output like this

  sl  local_address rem_address   st tx_queue rx_queue tr tm->when retrnsmt   uid  timeout inode
  0: 00000000:01BB 00000000:0000 0A 00000000:00000000 00:00000000 00000000     0        0 2891985097 1 0000000000000000 100 0 0 10 0

The second column (local_address) of the output shows the port in Hexadecimal. Use your Programming Calculator to convert the hex code to decimal.

For example over here, the port :01BB (in hex) is equal to 433 (in decimal) which is the HTTPS default port.