Russia lost a lot of their influence after attack on Ukraine.
Private citizens never even knew there is anything going in Ukraine, it had next to zero media cover and people were not interested in the slightest. Annexation of Crimea did not also interest anyone and did not basically affect peoples opinion on Russia.
Russian influence on Europe have probably never been lower than now. The media campaings they have had on Ukraine issue are so successful, that Russia is not very popular now in Europe.
US have lost its influence too, because of their current Administration and what they do and say, and how it is in formed in the Europe.
Pro-EU stance is growing among the European populace, and EU have never been this popular. First, US became very popular under Joe Biden because Russia lost its Influence because of what they do in Ukraine. Now US lost its influence and a lot of people are pro-EU.
When a person joins the European Parliament or any EU institute, they are pledging loyalty, and to advance the EU agenda. Not their national agendas. That is the purpose at least. EU is an institution that is outside of national governace, and as an institution, aims to grow in power. Of course many EU representatives have national agendas still. But this is all public information they state openly. That they demand loyalty to EU from their representatives over National loyalties. And that they aim to Expand. The newest additions will probably be Albania and Montenegro. North Macedonia wants in also but Greek is not letting them in, as you need the approval of all member countries. They have issue about their name, when Greek see Macedonia as their national heritage, and demand them to take the name Macedonia out of their country name. And North Macedonia will not, so they cannot join until this issue is resolved. Other than that, North Macedonia could be in already.
As for Euro, the more the member nations wreck their public economy, the more they are going to lose the independence on their economic policies because they do not control the central bank, but it is an EU institute instead. So the moment your public finances is seen as too bad, they have legal obligation to rein you in, and then you lose some of financial independence, which happened to Greek or example. The EU as an institute, and some pro-EU politicans within the countries might even want to see this happen. It centralizes power to EU over the national governments. Trough economic crisis you can centralize the power and this security situation is a fine addition too. Trough crisis EU as an institute, grows in influence and power, and trough hostile actions of other influental outside actors like Russia and US, their influence grows even more.
Georgia of course wants in, but its not much in the European area in the same way than others. Because they are expansionist, they have funded for a long time now some kind of support fund for Turkey membership transformation, but Turkey just takes the money in and is really not compatible with EU system and how i understand, is not even planning to be. They just want the transformation funding, but never plan to transfer, at least not this generation or maybe even the next. But for some reason they want Turkey in, which would seem rather a strange thought would they actually be a EU member country.
In case of Russia, there is not only the Russian influence on other areas. But other area influence on Russia as well. For example, i believe US have influenced Russian politics a lot. Russia started as a socialist or communist state under Soviet Union, but they have made a turn towards capitalism. Maybe on the influence of US. They started to privatize all of their national resources, privatized basically all of their oil infrastructure and so on with their "international partners" they later kicked out to nationalize most of them. The birth of Oligarchs came from the privatization, that they implemented in inside dealings for certain individuals, and then those individuals started to move away from Russia and spend their money elsewhere. The people were starting to want western products instead of Russian products, and Russian products have never been popular in Europe for example. Russian people used to come to Europe, and buy a lot of stuff because they like the European products more. So the western countries, EU and US had started to gain lots of influence in Russia. The situation might have now changed.
But i do understand, that US have affected Russia very strongly. And their capitalistic aspirations, privatization policies and so, are an appeasement to US and some kind of purpose to become a society that embraced the western capitalism. Russia after Soviet Union, have embraced capitalism very strongly, and that influence most likely does not come entirely from or within Russia. They have later tuned it down a bit, but it is still a capitalist system even now.
The modern Russians are capitalists. And their government is very capitalistic. Their origin is different. So also Russia have transformed. Probably more than US or EU. The one that have changed might be Russia, not the other way around. And Russia most likely is influenced way more by western countries than the other way around.
Russia understood very fast, that capitalism does not serve their interest. Because privatization leans to capital flight, their culture and products are not strong enough to compete with western ones and so on. They only deal with raw materials and for some reason, never succeed on producing anything that anyone want, other than raw materials and weapons. And the main selling point on weapons after the Soviet era have been that they are cheaper. Nowdays, they have a lot of more competition on their price point than in the past. In Soviet Era, there were basically two providers, US and Soviet Union, and the Soviet Union equipment was not necessarily worse, sometimes even better and more advanced. Now they have to compete with India, Turkey, China and so on. And more are coming, like Brazil, South Africa, North Korea and so on when they advance on technology. It also means, they lose these markets that in the past, bought from them. And China itself is maybe more advanced now than Russia and they are at the same price point, so people buy from there. Russia is losing big in one of their most important markets and no one ever even heard of other Russia products. So capitalism might not suit Russia well.
I do not know, how popular is the thought to join EU within Russian people ?
They at least have very similar system, and would be easy to transform to a member country if not taken in to account their military aggression and domestic militia type of aggression against their own populace, and political oppression of the opposition. Everyone does this in the EU, but there are rules on the way of doing it which Russia does not upheld. Suppressing any possible political opposition is of course the very first thing you want to do, but Russia methods on doing so are too open, direct and extreme for the EU. But the problem in that would be that no one wants them in anymore. In the past, many would have. Its a miracle if even 1 or 2 member countries would vote for Russian membership in the EU for many generations to come.
But would EU membership be good on Russia ? Maybe no. Because no one wants their product and they would need to open their market on stronger products, and their populace would learn to buy European, and not Russian products. Sanctions helped in this, but the populace still smuggle western products in because they want them very badly. They are seen as better, and people want them. If they are not better, at least they are marketed so, that people want them still.
Stronger culture and stronger product wins in open capitalism. Closed market and socialism, or communist type of system is better for those with weaker end products. And if you mostly sell raw materials, there is little reason to open your market. You only lose in doing so. And you cannot become a EU member without opening your market and establishing a free trade zone with other members.
The roots in Europe are socialistic, and many countries in the EU are very sosialistic on their ideologies even now. US have for decades tried to shift this towards capitalism, but many countries hold socialist systems and socialist political parties are very popular in many European countries. Some of them might even be more socialistic than Russia, and Russia might be leaning more towards capitalism than some of the EU member countries. So Socialism is not a problem on EU membership, almost all of the countries have strong Socialist support base already. In the US, they have none and they are pure capitalists. Most likely the only country in the world that is and a very successful one at that.
So the strange thing in this is, that if Russia or Soviet Union have wanted a more socialistic Europe. They forsake it, and turned to capitalism themself. So how can they influence others to become more socialistic, when they turn to capitalism themself ?
Even China is embracing Capitalism, but they are doing it in a way, that the US wont like. They want others to open their market to China, but want to more or less close their market for others. This is i believe, one of the things that the US is alarmed now. They want to start closing their markets for others at the same time, than trying to enforce markets for themself. But in my opinion, they are doing bad job on it, and will not achieve what they want in these methods that they use: Coercion, Blackmail and this kind. It will generate a response, and their influence and market pull will actually become lower.