One of my favorite BSD features is SIGINFO, which is intended for applications to give some sort of information about what they’re currently doing. If you’re on macOS, I know some of the copying commands (such as dd) implement it, and a ^T in your terminal will tell you how far along it is.
Huh, AFAIK on linux dd responds to SIGUSR1.
On Linux you can use progress¹ for many of these use cases. By default it scans for running processes that you might want to know about, but you can also ask it tell you about a PID with -p. It supports a -m[onitor] mode to report status until the command exits, and features some basic filtering options to ignore certain files.
You can also manually dig about in /proc/$pid/fd{,info}/ if you want something more fancy, like using gdbar² to display a graphical progress through files for a given process.