It's not Putin's love but China making Putin agree for having Pakistan in so that whatever investment in CPEC is not waste.
How's Paxtan to access INSTC. If it's via the land route , it'd have to go via Balochistan to Iran which is a headache for both Iran & Paxtan due to the instability there . If it's through the sea route they access Bandar Abbas or Chahbahar to transport goods then through Iran to the Caspian Sea & from there to Russia. In which case what's the point of Gwadar.
OTOH if the idea is to utilise Gwadar & from there to take it via the land corridor to Iran they still have to cross Balochistan which brings us to the first point. This is assuming Iran is open to such an arrangement which I very much doubt as it involves bypassing Iranian ports & consequent loss of revenue. In any case except China who's going to patronise Gwadar.
Finally what exactly is Paxtan going to export to Russia which it is not already though they could import a lot depending on the credit Russia extends them.
I don't see any future in this arrangement. It's just for optics & to boost both Russia & especially Paxtan's ego.