I suddenly noticed that Terminals such as gnome-terminal and xterm don't seem to forward Control-Tab. It's just a Tab. Therefore, Control-Tab key bindings cannot be used with Terminal versions of Emacs and Byobu. That's why it didn't work when I set the Control-Tab key bindings in Byobu. It's a shame.
Reference URL: https://askubuntu.com/questions/133384/keyboard-shortcut-gnome-terminal-ctrl-tab-and-ctrl-shift-tab-in-12-04
Although it does not forward, gnome-terminal itself recognizes Control-Tab, and Control-Tab can be set as a key binding to call the function of gnome-terminal. For example, you can set the key binding for switching tabs in gnome-terminal to Control-Tab. An example command to set is below.
gsettings set org.gnome.Terminal.Legacy.Keybindings:/org/gnome/terminal/legacy/keybindings/ next-tab '<Primary>Tab'