Emulate Colemak-DH when using non-English layout with modifier keys

Recently I’ve switched to Colemak-DH keyboard layout. I write multiple languages [English, Bangla (বাংলা)] on my system. Common keyboard shortcuts like Ctrl + C, Ctrl + V, Ctrl + Z, Ctrl + X, and other application specific shortcuts (more important) changed with the layout (shortcuts didn’t change, the position of most of the keys changed).

Now when I switch layout to Bangla, these shortcut behaves as if the system keyboard layout is QWERTY. For example, the letter ‘T’ is now on the position of ‘F’. If I press Ctrl + T, (position F in QWERTY) a new tab in browser should open. But when I switch my layout to Bangla (which does not have any latin characters), the shortcut acts as Ctrl + F (which is shortcut for Find in page).

Since Bangla does not contain any latin characters, I guess it’s the keyboard hardware that sends specific signals which Fedora does not convert to the preferred English layout.

Is there any way Fedora can emulate my expected behavior? (emulate the keys as Colemak, or preferred English layout, when combined with modifier keys like Ctrl, Alt, Super/Win, except Shift while using non-English layout) Or I need a keyboard that supports Colemak at hardware level?