The Soviet Union did not agree to invade Poland with the Nazis, it was about spheres of influence and red lines the Nazis should not cross in Poland. Spheres of influence were not agreements to jointly work together.

That's historical revisionism not even supported by Russian historians. That page is full of nonsensical statements too. On the page dedicated to "disproving" the secret protocols, it makes two claims:

• The secret protocols required that a Polish state exists still. Since the Germans destroyed it, the protocols were void.
• The Germans were talking about setting up independent states east of the demarcation line, so clearly it wasn't about partitioning Poland.

But the text of the secret protocols as I have linked already handily disproves both notions. First, it explicitly mentions that the question of whether a Polish state should remain is to be decided later; clearly this means that the existence of Poland itself is not a precondition for the protocols holding. The protocols also basically outline "what happens after Poland is invaded and how should it be divided", you can call it a partitioning into spheres of influence if you like, but the protocols did not care exactly what the Soviets or Nazis would do on either side of the line, annexation, puppeting or otherwise. All that mattered was declaring where belonged to who. That's colloquially known as a partitioning.

The setting up of independent states east of the line is also not proof of anything. This was being considered before the USSR invaded, and the Germans needed to decide on something with the remaining land. They opted for independent countries over puppet governments or direct annexation, so as to leave the area to the USSR to deal with.

Ultimately both countries invaded, and the Nazis retreated back to the demarcation line.

Should the Soviets have let Poland get entirely taken over by the Nazis, standing idle? The West made it clear that they were never going to help anyone against the Nazis until it was their turn to be targeted.

The USSR was aware of the defensive pact between the west and Poland, and the west declared war on Germany when they invaded Poland.

Further, you're ignoring the Munich Agreement, where Czechoslovakia was given to the Nazis by the west. Not only was the west on good terms with the Nazis, signing many non-aggression pacts, they fostered healthy relationships.

The west was still on appeasement mode (which was a mistake in hindsight). But they were not on "friendly" terms at all, clearly evidenced by the fact they were still negotiating with the Soviets to form an alliance against the Germans. The west was actively negotiating treaties to contain Germany where possible, but not all countries targetted by the Nazis agreed to one since they were worried aligning against Hitler would make them a target (the concern of the Baltics for example).

Finally, the Soviets were reasonably highly suspicious that Britain and Germany would ally. This was not unfounded, both were friendly enough until the outbreak of war. The Soviets desperately needed to make sure that the British and Germans would not ally, which reasonably would have happened had the Soviet Union taken unilateral action against the Nazis, rather than waiting to be attacked first.

This was, as far as I could find, never a Soviet concern. They did not believe the west would ally with Hitler, rather they were mistrusting that the west would let the USSR fight Germany on its own, weakening both states. This was actually the same concern the west had, they feared the Soviets would pull the west into a war against Germany without a cause they could support. This deep mistrust was a key reason why the triple alliance failed to materialize. Ultimately it was the west that declared war on Germany first, and the Soviets indeed let them fight before being forced into the conflict by Germany.

This is ignoring the secret protocol in which the USSR and Nazi Germany carved up eastern Europe into spheres of influence: https://avalon.law.yale.edu/20th_century/addsepro.asp And yes it does mention carving up Poland, it describes what the border should be if Poland is invaded (wink wink) and then declares that leaving a Polish rump state or not will be decided later. It also in no uncertain terms states that the Soviets can take Bessarabia.

It is the only non-aggression pact with such a protocol. The western powers did not sign such a deal with the Nazis in which third-parties are carved up.

Negotiations between the west and the USSR broke down for several reasons, notably:

• Deep mutual mistrust, in part due to the mass terror and the purges in the USSR, and notably France failing to make good on an earlier promise for a military agreement. Both sides believed the other might abuse a pact to draw them into war with Germany.
• Disagreement over the Baltics; the USSR believed Hitler would attack through those states, but the west did not want to commit to security guarantees to states that did not want them (Estonia and Latvia rejected them, fearing it would incense the Germans).
• Once the west finally yielded on guaranteeing the Baltics, the USSR refused to do the same for the Netherlands, Luxembourg and Switzerland.
• The USSR demanded that in case of war, the Red Army would be given free passage through Poland and Romania. The west told the USSR that they'd have to negotiate that with those countries themselves, and they could not unilaterally allow it without having either country agree.
• There was disagreement over what would constitute "indirect aggression", eg what the Nazis did to anschluss Austria.
• The USSR kept hammering on immediate, unconditional action in case of war with Germany. The west wanted consultations first, as they were worried the USSR would do something in the Baltics to trigger war with Germany, drawing the west in for a cause they might not support.
• The west had little motivation to push for a pact, as it had already provided security guarantees to Poland and Romania. The only other land access route was through Memel into Lithuania, but Lithuania had ceded Memel and signed a non-aggression pact with the Germans, so the west did not think an attack over the Baltics was as likely as the Soviets believed it was.

Ultimately the security guarantee on Poland brought the west into war with Germany. The USSR, despite hammering on immediate action against Germany during negotiations before, instead opted for the annexation of the Baltics, Bessarabia and eastern Poland, and an attack on Finland. It took nearly two years for the USSR to begin fighting the Nazis, and only because the Nazis invaded them first.

No notes on Churchill being a dickhead though.