You don't need much of a historical deep dive to see how it's currently being used:
> The term Little Russia is now anachronistic when used to refer to the country Ukraine and the modern Ukrainian nation, its language, culture, etc. Such usage is typically perceived as conveying an imperialist view that the Ukrainian territory and people ("Little Russians") belong to "one, indivisible Russia".Today, many Ukrainians consider the term disparaging, indicative of Russian suppression of Ukrainian identity and language. It has continued to be used in Russian nationalist discourse, in which modern Ukrainians are presented as a single people in a united Russian nation. This has provoked new hostility toward and disapproval of the term by many Ukrainians. In July 2021 Vladimir Putin published a 7000-word essay, a large part of which was devoted to expounding these views. [0]
Ethnical slurs, or any other slurs, change over time. If you go back in time 100+ years in any context, and you use a modern ethnic or racial slur, it will most likely empty of meaning. Just like a lot of slurs from the past have lost their meaning over the years. But the "historical meaning" is constantly being used by Russian propaganda, where they claim one needs to go back to the 1200's, and their interpretation of history, to try to make sense of the current genocide attempt in Ukraine.
There's no logic behind that approach because current actions speak for themselves, including the context of recent history, and that's enough. You can get a pretty clear picture of this whole event starting in the 1990s.
Unless you still see that slur being used by Russian nationalists as an endearing term to address their "brotherly nation" which they support being erased from the map.
[0]https://en.wikipedia.org/wiki/Little_Russia#Modern_usage