The (misguided IMO) idea was that buying their gas and integrating them into world markets would strengthen ties and liberalize them in the medium term.
Nobody believes that anymore, post-2022.
I don't think it was misguided; Nuland-Pyatt leak and the tapping of Merkel's phone made it pretty clear to me that like in the Yeltsin years the problem was that the US didn't want Russia/Europe ties to succeed.