Well, the treaty is probably reluctantly signed. The USSR becomes greatly decentralized, with only military and foreign policy being directed from the imperial center. The rest depends a lot upon what Yeltsin does. He's still the President of Russia, and according to the new treaty version of the USSR, he has more say in Russian domestic policy than Gorbachev did. Now if Yeltsin doesn't do anything differently here, there's a distinct possibility he's thrown out in 1993. There is no way Gorbachev is going to allow the Army to save Yeltsin's Presidency.
But with Gorbachev still in a position of relative power, Yeltsin may be inclined to shore up his support with the Russian legislative body. I know traditionally such bodies meant basically nothing in the USSR, but remember, the new USSR is not the old. It's basically a collection of independent countries that happen to share a military and foreign policy via an imperial center. I remember once reading an argument that Yeltsin made a major error in not calling an election in 1991. So Perhaps the whole drama in 1993 never happens here.
Even without the white house incident, Yeltsin still probably has some populist support here, this is 1991 not 1996. So maybe he calls such an election to make sure his support within the Russian government is enough to protect him from Gorbachev. Domestically, I see very little policy wise changing in Russia, unless Gorbachev somehow ousts Yeltsin, which before 1993 or so seems unlikely. Like I've said before they hated each other, so there is going to be some tension there. I doubt the New Union will break apart in 1991. But there's always a chance that the Yeltsin vs. Gorbachev fight could lead to the "Imperial Center" being done away with at some later date. I also don't know how long Gorbachev can last as the "President of the USSR" Down the line, assuming that there isn't a break, the biggest possible difference I see is that there might not be any Chechen wars.