Pretty sure that's how dbm handles it, when you shift click a timer announce it to whatever channel you had active last. Announcing timers into say chat is not useful in most cases.

Yes.

It seems strange to me for the shift click behavior to be different from both dbm and bigwigs normal actions. If anything were to announce to say wouldn't it make more sense for it to be the ctrl click instead of shift click?

You don't need to use a modifier with BigWigs. But if you do, the default is Ctrl, which is the same as Capping.

Capping will announce depending on which modifier key you use:
https://github.com/BigWigsMods/Capping/blob/master/core.lua#L559-L575

Use CTRL + Left Click to announce it to the instance chat or raid.

Edit: Initial response was wrong.

Never thought to ctrl click, does it make sense to even announce to say in any case tho?