I'd imagine you can use a keyboard shortcut as well to open this menu, but based on the text cursor, rather than the mouse one.

I do this a lot is vscode to auto-fix issues and automatically add imports for the identifier under the caret. It's however frustrating in that it sometimes uses the underlying platform's dropdown widget, which doesn't respect my key bindings (Emacs-like, using C-p, C-n for up, down etc).