the first 2 screenshots show page editing normal and broken (no picture of the page, code only) and index editing (broken first, and normal with menus and input cells).

Thanks for the quick feedback here and screenshots. :-)
So it might be the case, that the TwoColConflict extension messes with the hooks there when enabled.. Then the special editors on WikiSource do not apply. I am not sure how fast we can fix this. As a workaround you should probably deactivate the extension in the beta features when you want to use the special editors :-/

Ups, yeah we have already a ticket for that, will close this one as a duplicate