I don’t know what the people of Belarus want, but the political leadership apparently has been very pro-Russian. Lukashenko has been in power since 1994 and from what I have read runs the country in an authoritarian way...so not much has changed since Soviet times apart from not having to spout Marxist-Leninist rhetoric. Both the Belarusian and Russian languages are official...the Belarusian language is close enough to Russian that some consider it a dialect of Russian. (Its version of the Cyrillic alphabet has two letters not used in Russian Cyrillic.)
I believe Russians are generally happy. Belorussians are not. Something has got to give there. They do not have the big country super power mentality that Russians do. They also have a front row seat to the explosive growth the Baltics have had in the post soviet period. I expect sooner or later Putinist Russia will reel them in by force. Like Ukraine onne party state fascist Russia can’t have a western leaning and prosperous Belarus lest Russians notice the raw deal they are getting.
Most Belarusians speak Russian. The country was an orphan when the Soviet Union disappeared.
They’re in the Eurasian Union for political and economic reasons. And they’re dependent on Russia because history put them right next to a powerful neighbor.
The country has no real option for true independence.