Which then begs the question of why, and also, how does the US. NATO and EU benefit from the current Polarization in the world. Why do we want this polarization and how do we benefit from China (and others) being put in a position where they have to refuse to condemn Russia's actions?
NATO benefits from a renewed sense of purpose but this is due to Russia's starting a conventional war to conquer neighboring territories, something that NATO is designed to stop for its members.
For the US and EU, there's not really much benefit, economically everyone is still recovering from the COVID problems. The US and EU would love to have no conflicts and just truck along making money so the increased tensions really are harmful, especially as the various global corporations try and resolve even more disrupted supply chain issues.
I think the only real benefit to this polarization is in granting more credibility to those like myself that keep stamping the floor and saying that authoritarian regimes like Russia and the PRC are threats to our way of life and we need to limit our exposure to them lest we be forced into an untenable situation in the future.

Is this an attempt to put everyone in the same basket and say "hey look, Russia is the big bad wolf and anyone else's that supports it" so that China becomes a target too in the eyes of the world?
Russia is being targeted because of what it did, China, India and a lot of other countries are trying to hedge their bets on both sides. CHina however does have a vested interest in the success of Russia as it is its only significant ally in the world. China made itself a target though when it started to try and force its claims on its neighbors like India as well as throughout the South China Sea with its aggressive 'grey zone tactics' using maritime militias and building islands on atolls to reinforce its claims.

What is the goal here? Is this an indication of the US & Co failing for Thucydides Trap leading us towards an eventual armed conflict where the whole world is mainly split in between the two and will end in Armageddon?
The US and its allies generally bend over backwards to avoid war with its larger rivals. Honestly, the big danger is China assuming a lack of resolve on the part of the US in supporting its allies. The view of the US and the West in general as 'paper tigers' was the same mistake the Imperial Japanese made.

Or a new Economical reality? Do we realize that Russia, China India, South Africa and Brazil alone constitute half of the word's population? What is the goal here to split the global economy in two separate financial, banking and trading systems?
Of course those countries are hugely populated and important, if they don't want to work in a 'rules based' world system and instead go back to the times of 'might makes right' then that's on them. The goal of the US and West in general has almost always (post cold-war) been one of more or less 'open for business' through increased trade and business. The divestment of the West's industrial base to east and south Asia is proof of that.
It's less a split of the economy into two spheres (which we already had in the cold war anyhow) but into a determination of how countries should interact in the future. Economic measures and sanctions are surely preferable to military measures and blockades, right?

I really think that we need to put a collective and to Geopolitics period lest we risk to lose our Human Civilization. I really think that we have to shift our minds and put people value above some arbitrary border delimitation on a map and above the value of the land these people live upon.

We need to put lives above materialism, we need to end Greed and Lust for Power and start thinking before whom we vote in to power seriously and for what Agenda. We may even need to change our Democracies to be more participatory structure and decision making, the technology is there to do so, lets use it, for the benefit of the many and stop being used by it for the profit and benefit of the few. And for an earth whose inhabitants live in peace and prosperity equally with one another and in all our diversity as one Humanity.
These are nice ideas but how do they get implemented? This is like saying that the way to end violence is everyone just disarms and stops fighting, how does one make the entire species to that?
Transcending borders and economics is something to aspire for but not realistic in the current environment. Even the friendliest of cooperative groups like the EU struggle to work together, doing so with other regional groups is even harder, that's why the UN is sort of just window dressing as it essentially powerless unless the security council advocates action all together.