There are other ways to do things. Russia's methods are aggressive, unnecessary, and frankly just have some significant downsides that prevent others from pursuing a similar path, at least today.
Russia cannot woo others economically and politically, whether if it's its own fault or not, and it likely will never be able to do so while positioning itself as an opponent to the wealthier, free-er west, especially in the age of the internet where everyone can see the relatively much better life in the west.
But then, its decision to reject a western lifestyle and prevent its citizens from having that, is still, in the end, its own decision, and the consequences are quite clear - political entities in the global arena will be more polarized, and its "allies" will be more puppets than actual allies that feel truly compelled to help in times of need. It and its allies will also be less capable of helping one another because of the isolation from the wealthy west.
Countries of importance to Russia will either fear it and join it as puppets, or will be drawn closer to the west out of a notion they can deter Russia with some help.
So although Russia's strategy to reoccupy the former Soviet Union states is logical, its endgame strategy isn't. And the former is a result of the latter.
Bottom line is Russia does not do what's absolutely necessary vis a vis Ukraine. Neither with Georgia, Belarus, Moldova, Kazakhstan, etc. A more peaceful approach would almost certainly yield far better results, even without the aspect of relieving Russia from economical sanctions. Its long shared history, familial bonds, and cultural bonds, can certainly keep the former allies tethered to it, as well as the benefits of geographical proximity, large population (customers) and abundance of natural resources. To do that, Russia may need to westernize, but everything we see today is the result of its decision not to do so.
I think you're mistaken on several points.
In principle Russia doesn't reject the "western lifestyle". Russia today is a capitalist country by any reasonable definition. However lifestyle requires economic prosperity, and in a way so does democracy. This is where some issues stem from. The closest Russia got to a middle class demanding democratization as a group were the 2012 protests against Putin's 3rd term. Note how limited in geography and scale they were. (on a side note I think Putin made a mistake going for a third term, I think he should have remained prime minister or even stepped into some grandfatherly role like head of the Security Council)
Russia also does offer economic incentives to friends and allies, including beneficial trade arrangements and even major discounts on the prices of oil and natural gas. The Belarussian economy, largely unremarkable, has done so much better than Ukraine in part due to the discount on oil and has it enjoyed for many years. Today consider the price for gas Serbia with it's pro-Russian leadership enjoys vs. Poland. However in the case of the Baltic States, or Ukraine, I don't believe any Russia that isn't weak and divided would be anything but a potential threat to the political elites in those countries. Ukraine in particular is still run by the same kinds of robber-baron oligarchs that ran Russia in the 90's. To them the problem isn't Russian aggression. It's that any stable and prosperous Russia is a bad precedent for their own rule. The one thing they fear, and have feared since the early 2000s, is that either the Putin or a home-grown Putin will take over and put an end to their oligarchical clans, or at least severely reign them in. This is why Ukraine is willing to go against economic common sense, against a large chunk of its own population, and certainly against public opinion (consider polling data on the language question in Ukraine and compare it with the government stance). Ukraine's elites have effectively nothing to offer their own people and they know it. Which means that unless they can build a highly anti-Russian ideological framework, they always run the risk of either a domestic pro-Russian strong-man, or actual Russia, ousting them.
Georgia is a separate situation where an existing, internationally recognized conflict in the country, based on ethnic cleansing committed by multiple sides but initially started mostly at the prompting of Gamsakhurdia, brought the country to the brink of a Yugoslavia-style dissolution. In the mid-90s the arrival of Russian peacekeepers had a lot to do with keeping Georgia together as a country. And it's mostly the rise of nationalism, and Saakashvili specifically that led the country down a road to war. Remember Saakashvili's relations with Putin only soured after he swallowed up Adzharia and broken promises that he made. Had he allowed the Adzhars to keep the autonomy that was negotiated, he likely would have been allowed to re-absorb South Ossetia as well (though I suspect Abkhazia would be far more resistant to this).
I believe Russia very much wanted to be part of the collective west in the late 90s and early 2000s. However what Russia was thoroughly unsatisfied with is the role of a colder Saudi Arabia with nukes. Russia saw many countries enjoying spheres of political and economic influence (France in West Africa, or the USA all over the world) and believed it should have one too, for the obvious political and even more so economic reasons. There was still some lingering mistrust of western intentions, and NATO itself had been an adversary for such a long time that seeing them as anything but was challenging. NATO actions in Yugoslavia, without a UN mandate (including encouraging the Chetniks in Croatia) and US actions against Iraq, were all seen as precedents by Russian leadership and elites. And some of the lessons they took away were that if Russia were ever in a Yugoslavia-like situation vis-a-vis the North Caucuses (for example) and didn't have a credible nuclear deterrent, it's entirely conceivable (to them) that a US-led NATO force could intervene on the ground, and bomb Russian cities as part of a campaign to force a political resolution favorable to the west. Despite this not entirely irrational fear, I believe there was still a genuine desire to integrate with the west, but only on terms of equality. And this is where friction began in large part between the doctrine of US exceptionalism, as the sole surviving super power, and Russian insistence of a complete absence of
any US exceptionalism, except such as is codified in existing international structures (UN Security Council membership for example). In other words, if America is allowed to invade Iraq on a fictional pretense of WMDs, and engage in whole sale regime change, why isn't Russia allowed to do something similar? If America is allowed to fund political movements aimed at promoting US agendas in other countries, what's wrong if Russia does it? Why is it that when the US does it it's "democracy promotion" and when Russia does it it's "meddling in the affairs of a sovereign state"? In my opinion this is where distrust of the US, and US-led institutions such as NATO grew steadily throughout the 2000s. The BMD discussions did nothing to help the situation and the attempt by western media to portray the 2008 war as just a Russian aggression didn't help either. You'll notice during this time that Russian relations with individual European NATO members differed wildly from Russia fear of NATO as an institution, and Russian friction with the US.
