It would require entire society entering into postcarcity era. Technology which is basically magical at our current level of development. And note that while Federation is very advanced socialism, maybe even functionally be called communism, but it was established in very utopian way, first by world war destroying enough capital to basically eradicate capitalism and soon after by the alien tech transfers of abovementioned technology, so that the capitalism didn’t reformed itself. And that transfer was basically result of one super genius constructing warp drive (another magical tech) in his own spare time.

I would say the only real way to reaching what Star Trek shown us lies through the revolution and establishing the proletarian state which would advance society and technology to reach the postscarcity.

we will assume that the universe and our environment are capable of supporting life outside the Earth. At the moment of our enlightenment with this information, humanity will find itself at a turning point.

We currently lack the tools, but those are actively being developed. New planets are being discovered constantly. But the question of “supporting life outside of Earth” is not that simple. We would need to go and check first, because even seemingly paradise planet full of life might be as useless as barren one if that entire life have minimally different base biology, etc.

Abolish the self-destructive economic hierarchy of the world, destroy the social constructs that keep us in shackles, or remain just one broken world of semi-sapient monkeys.

No. If that was this simple to do, just abolish entire production system out of hope to build a better world, even something like religion would do it long ago, after all, aren’t they vocally seeking exactly that and have great influence?

Are the ideals of the Federation compatible with the ideas of communism?

I think yes. Though note that while a lot of westerners think Federation is something very libertarian in it nature, it’s pretty clear that they value organized society and central planning.

Another point is that Federation is not stricte a communist society. It is assumed moneyless, at least on developed worlds, but we also seen some things like usage of labour tokens equivalent and markets existing here and there with currency. Classless, seems like it, though since we are shown very little about Federation society, i don’t really know. Extraterrestial cultures also complicate things. Stateless, it isn’t - Federation is actually a state, obviously for the reason that in universe where Klingon Empire, Cardassian Union, Romulan Star Empire, Ferengi Alliance or Borg Collective exist, state is necessary.

I would say that ironically for all its utopian markings, Federation is pretty close to the idea of USSR, a socialism in one state, but it is union of former states willingly joining for mutual benefits.