I've trimmed down the interface and removed all of the plugins that I didn't need. However, the "Code completion Toolbar" has an extremely wide fixed-width. I found that it can be resized from "Settings -> Editor... -> Code completion -> Symbol browser (tab) -> Toolbar -> Scope/Function choice length".
This is still only a workaround as the space available varies depending on the size of the window, full screen, etc.
It would be nice if this toolbar would resize itself as necessary rather than being truncated by the size of the window on a percentage. For example, change the length option to a minimum with an additional option for "Automatic width bias" favoring scope. So, a bias of 50% would use all of the available toolbar with half being used for each combox. A bias of 30% would instead use a width of 30/70, but also honoring the minimum width.
I'm new to Code::Blocks and would be happy to look into submitting a pull request for this myself if someone would be kind enough to direct me to the relevant sources.