Sorry if this is a vague question, but essentially I want to know if the Ruthenian people (Or Lithuania, where most of them were based at the time) actually had aspirations for a non-Russian Rus during the early modern period, or anything later if that's likely.
If the answer is yes, bonus question, was this dream realistic?
Ruthenia is an English version of the Old Russian word Рѹ́сь (Rus') and is in fact more geographic term applicable to the lands of old Kievan Rus (words Russia and Russians are derived and superseded it ). At the time EU4 starts there was in fact few Ruthenias- the Black Ruthenia (early conquests of Lithuanians: Hrodna, Slonim, Volkovysk), the Red Ruthenia (lands taken by Polish in 14th century: Chełm, Halicz, Lwow) and the White Ruthenia ( Polotsk, Vitebsk, and Mahilyow). In 16th century the territories named by this colors shifted- at least according to Maciej Stryjkowski: White for Moscovite, Black for Commonwealth and Red for the rest (at that time- Novgorod).
Byzantines used term Greater Rus’ and Little Rus' for metropolitanates of Muscovy and Halich and this terminology is- unlike colored one- is still in use Greater being applied to the Russia and Little to the Ukraine and Byelorussia.
if the Ruthenian people (Or Lithuania, where most of them were based at the time) actually had aspirations for a non-Russian Rus during the early modern period, or anything later if that's likely.
The Kingdom of Ruthenia predates both Muscovy and EU4 timeline. founded by Daniel of Galicia in 1253 it was major powerhouse of that time, but was carved between Poland and Lithuania after 1323.
In the early modern period the closest thing to that would be Cossacks. Even at best of times they there subjects of Commonwealth only nominally and with Khmelnytsky Uprising a Cossack Hetmanate was established as de facto indepented country. After failing to ally with Ottomans, Hetmanate become an autonomous protectorate of Russia in 1654 (Treaty of Pereyaslav).
Poland-Lithuania tried to retake losses by promising to establish Duchy of Ruthenia as equal part of Commonwealth of Three Nations (Treaty of Hadiach in 1658) but idea was soon abandoned.
Cossack Hetmanate was disbanded after they allied with Sweden in Great Northern War in a bid for independence.
However, Ruthenia in EU4- I think- is based on Daniel's kingdom with Cossacks being they own thing.