Thanks for the exhaustive answer! Any pointers as to where can one learn more about this stuff?

Great to see someone who has actually seen the sausage machine from inside. What I always wondered about how the dynamics between the parliament and commission looks like. Parliament doesn't have the right of initiative, so it discusses proposals made by the commission, suggests changes, sends those back to the commission etc. So far so good. But how does it actually work beyond that? For example, given the missing right of initiative, can the parliament blackmail the commission into making a proposal they want by refusing to approve other, possibly unrelated, proposals?  How does the council interact with the parliament? Can parliament team with the council against the commission? Or maybe the commission and the council against the parliament? What about the citizen's initiative. Can the parliament adopt such initiative and propose legislation? Etc.

What are the concrete policies to advocate for? What are the biggest hurdles that Russian emigrants are facing at the moment? AFAIK, it's only Baltic countries and Czechia which stopped granting  visas to Russians. It should be possible to get a visa in other EU countries. Would granting vises on arrival (as opposed to getting it in advance) help? Is transfer of money outside of the country the biggest problem? Is it limited air flights opportunities? (I hear it's still possible to get to Europe via Serbia.) Is the problem rather with turning the visa into residence permit? Or maybe getting a work permit?

US is a big country and doing anything is hard and may take a long time. It may be easier to sway small countries.  It you are trying to escape a small country is as good as a big one.