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.