How to bind “Ctrl-Alt-b” as the prefix of tmux

You want select-pane:

bind C-l select-pane -L
bind C-h select-pane -R
bind C-k select-pane -U
bind C-j select-pane -D

Ctrl and Shift are modifiers. These keys aren't transmitted to applications running in a terminal. Rather, when you press something like Ctrl+Shift+A, this sends a character or a character sequence at the time you press the A key. See How do keyboard input and text output work? for more details.

There may be some terminal emulators that can be configured to send a key sequence when you press Ctrl+Shift, but even that isn't a given and might depend on which order you press the two keys in, and you'd lose the ability to make Ctrl+Shift+key shortcuts.

If your terminal emulator permits it, you could configure it to send C-b a when you press Ctrl+Shift+A and so on. That would allow you to use single-keychord bindings for some commands.

If you want to free the keychord Ctrl+B so that it's sent to the underlying application, pick a different prefix such as C-\ or C-] or C-^.