The status bar is updated after each edit, so things that show in the status bar are all values that are updated automatically, mostly as a side effect of other functionality, like lines being available because the editor keeps per line data for display purposes, same for position etc. These are updated as editing happens because they need to be. So they are available to be displayed after each edit.

But nothing keeps track of words or characters as editing happens, the tools menu has to go scan the whole document to count words and characters (Unicode code points, not bytes). But scanning the whole document each edit is likely to be expensive and most users won't want it, words are not useful to code editing, that main target of Geany.

So this is the sort of thing that should be in a plugin so only those that want it enable it.