If the USSR had chosen not to divide Central Asia into multiple SSRs and instead did just one big "Turk SSR" then the national images of Kazakhs, Turkmens, Kirghiz, and Uzbeks might be lessened compared to 1991 OTL. The Tajiks however are going to be a minority related to Afghans and Iranians and will disassociated with the Turkic majority. Either you have a South Ossetia problem or you can have that the SSR has the Tajiks as their own SSR and then the 4 Turkic majority are in the Central Asian SSR.
If that's possible then based on uti possidetis juris, which is the prevailing international legal norm recognized by the UN and US, even China would have no choice but to recognize the national government of a united Central Asia as inviolate, and few if any would ever recognize any subsequent breakaway republics based on tribal allegiances (such as Uzbeks or Kirghiz). They'd be seen as no different than Trans-Dniester, South Ossetia, Chechnya, or the Serbs breaking away from Bosnia et Herzegovina. There's a reason Kosovo has been taking so much longer than the initial breakup of Yugoslavia.
In international relations however I don't see that a united Central Asia would have any different relations with China, Russia, or the US as Kazakhstan has had. China will of course want a sphere of influence on a large state on their western border that has religious, linguistic, ethnic, and cultural ties to a large part of their western region. Russia will want a sphere on a former "colonial territory" that has a large Russian minority, secure their southern border of Siberia, contain China, keep US out of being so close. The US will want to be there to maintain control of the skies of Asia and for transport logistics, and to contain China and Russia.
Afghanistan and Pakistan could never join, other than being Muslim they have nothing in common being Indo-Iranian. Tajikistan probably not for same reason though at least historical and some cultural ties are there. Turkey probably becomes a big supporter with cultural exchanges. I don't see the larger country being any more important or stronger than OTL Kazakhstan is though. Perhaps the Aral Sea ends up being better off environmentally, but it could very well end up being worse or no different than OTL. Central Asian unified won't go up against the PRC and support any breakaway Uygur terrorists or anything like that.