The shell obtained with nc is basic. The completion with Tab, the history with arrows are not managed.

Put the nc in the background with:

Ctr-Z

Then ask the current shell to pass the raw keystroke codes to the remote shell, and switch back to the netcat (foreground)

stty raw -echo
fg

Disclamer: Trying this in a browser will just freeze the shell. The browser also modifies the key codes. It only works in a VM