@Iniquity I'm not sure I understand the request here. MediaWiki:Sidebar has only ever allowed customization of the content of menus not the labels.

Some of the red boxes you have drawn (vector-main-menu-label and vector-page-tools-label) are not menus but controls for those menus and are outside of what we consider the sidebar. Adding support to MediaWiki:Sidebar would be a little unexpected and counterintuitive to me in the same way it would be counterintuitive if
nstab-project message could be controlled by MediaWiki:Sidebar.

Regarding the red boxes inside the menu (vector-page-tools-general-label and vector-page-tools-actions-label) - it's not possible in MediaWiki:Sidebar to replace the toolbox heading. It only supports a TOOLBOX keyword to allow control of the position (and by cooincidence the associated message is toolbox). I am hoping with : T318435 we'll also support reordering the page tools menus e.g. allowing TOOLBOX to appear above ACTIONS but I don't see how or why we would add customization of the message keys themselves.

https://en.wikipedia.org/?useskin=vector&uselang=qqx

it is very difficult to access the strings that need to be translated.

It seems in this case you used ?uselang=qqx which is precisely how we encourage customization of the menu. If those messages can be further modified by SIDEBAR isn't that adding unnecessary complexity - as now you'll need to check multiple message keys for a single message. I'm not understanding the difficulty here. Could you elaborate further?

Hello! Maybe you are right and I was just too surprised that some of the messages appeared in English. It's just that most of the sidebar used to be controlled MediaWiki:Sidebar including the headers. Therefore, the first thing I did was get into the MediaWiki:Sidebar, and only then did I start looking through &uselang=qqx. Just in one essentially the menu - two different behaviors. And it's not entirely clear, maybe you just need to get used to it. If you do not see this as a clear problem, then we can return to this later.

It is confusing to see mixed languages in these columns.