I'm going to answer different parts left unanswered by @hschou.

So, I have no way to know if the scp process is still running or how much is remaining.
Could we get the display of the running process back on my terminal?

to get a list of running processes you can use command ps

ps aux | grep scp

To monitor it, you could use command watch or just do a simple loop yourself

while true; do clear; ps aux | grep scp; sleep 5; done

This will run ps aux | grep scp every 5 seconds.

I'm going to answer different parts left unanswered by @hschou.

So, I have no way to know if the scp process is still running or how much is remaining.
Could we get the display of the running process back on my terminal?

to get a list of running processes you can use command ps (man page)

ps aux | grep scp

To monitor it, you could use command watch or just do a simple loop yourself

while true; do clear; ps aux | grep scp; sleep 5; done

This will run ps aux | grep scp every 5 seconds.