There’s yet another point to consider.
Stalin only considered UK & USA as Allies of the moment. As soon as combat in Western Europe ceased, both were again enemies of the USSR, as Stalin viewed it.
Warfare is also an economic activity, and the UK and USA having to fight a war on three disparate fronts (Europe NthWest, and Europe Sth, Pacific and Asia), whilst still having to supply the USSR via Lend-Lease as well as account for the wellbeing and governance and feeding of the civilians populations in the frontline territories were all vast economic drains.
Whilst in effect the USSR was having to fight on a (by comparison) unified front (Ukraine, Baltic States) whilst the UK & USA were fighting on disparate fronts was thus a greater economic drain on UK & USA .
Once the UK and USA economies were sufficiently weakened, neither would be in suitable position to resist the USSR once and if it (Stalin) were to be decided to invade Western Europe following the defeat of Germany and Italy. There are indicators that such was in fact the case: consider that Germany itself once defeated became hostage while the USSR developed it’s own Atomic bomb under conditions of extreme urgency between 1945 and 1949. The later Berlin Airlift is also integral evidence of the hostage status of defeated Germany.
Where Italy plays into all of the above is the necessarily economically draining nature of the superbly defensive terrain. It costs per soldier on the ground a hell of a lot more to keep him feed, alive, and maintained in ammunition and medical supplies in terrain such as Italy, than it costs to keep that same soldier similarly supplied in flat open plains such as Poland or the Ukraine, or indeed the Taiga or Steppes.
Thus, Italy was not only a politico-strategic consideration, it was also an economic drain of larger proportion than the actual strategic worth of the terrain itself.
As such, it is the “second front” (yet relegated to third, see below) Stalin sought to have, but yet is relatively minor in comparison to the Normandy front, which rightly takes the term “Second Front” by virtue of greater strategic importance to the UK & USA.
Kind and Respectful Regards, Churchill my friend, Uyraell.