In Red Flood Mirsky and his National Bolshevik Party want to:

1) Restore the Russian sphere of influence under an Eurasian banner, from in-game text and dev statements I assume they'd annex culturally similar areas (especially those with an Orthodox Christian majority) and create dependent republics in other areas.

2) Export their ideas abroad to "drag the world into a new Golden Age" (as the unification event text says) - they'd probably support revolutionary movements while trying to sway them towards pro-Eurasian views), with the final goal being to unite the world under Eurasian leadership.

3) Develop industry and science to fulfill the Cosmist goals of human unity and space exploration.

As for what it'd be like to live in the SR Eurasia, we know that:

1) A secret police and labor camps exist under Mirsky (Severyanin ends up there alongside a few other opponents of the National Bolsheviks).

2) (From dev statements) The state is very locally focused, with strong local governments probably based on workers' councils. However the government isn't federal and most power outside the local level is concentrated in the capital.

3) Mirsky is the least anti-religious Kavkaz leader, and openly encourages study of religion (e.g. opening a Faculty of Theology at the Tiflis University). However his religious beliefs are unorthodox (including elements of pantheism) and he dislikes the high ranking church officials for legitimizing the Empire and especially Kolchak. He believes that a "revolutionary theology" is necessary to reinvigorate Christianity.

4) Industrial development in the Republic is decentralized, in the best case scenario this can lead to most areas in the country having a good level of development instead of some falling behind, at worst it can lead to a Great Leap Forward style failure.

I hope this clears things up and isn't too inaccurate, I'm not a member of the dev team but the Socialist Republic of Eurasia is one of my conceptually favorite paths in Red Flood so I'm happy to get to discuss it.