The new Imperial Russia seems about as democratic as the late 19th century United Kingdom. The monarchy still has great powers but rarely acts independently of the elected government. Like Queen Victoria, Tsar Vladimir III usually defers to the elected governments and acts like a figurehead publicly but wields a fair amount of behind the scenes influence. The Tsar's words are no longer unquestionable commands but any sensible elected politician should seriously consider the Tsar's requests and attempt to remain on the Tsar's good side. Like the 19th century UK, the power of the state religion over politics has been greatly reduced and non-believers are no longer actively persecuted but one should be at least a nominal follower of the state religion if you want a high office.
Imperial Russia and her alliance bloc are powerful but not as powerful as the OTL United States and its NATO alliance. It is a multipolar world here. Russia also has weaknesses that the OTL USA did not. There is a direct land connection between Paris and Petrograd and mainland Russia is at direct risk of being invaded by French tanks. There is the risk of a two-front war if Japan decides to take revenge in a WW3 situation. French and British agents might attempt to inflame the anger of the sizable ethnic minorities in the autonomous regions to undermine Russia's efforts. The Third Internationale might be more powerful than the Warsaw Pact because they control the more industrialized western Europe. Russia also has to decide if her bloc is a group of allies or a network of Russian puppet states soon.
The Entente Cordiale is the weaker third bloc of this world. They are Russia's natural allies against the Third Internationale. Are they still at war with the syndicalists? They lack the power to retake Europe without Russian help. I expect periodic naval clashes in the Atlantic. The Entente and Russia should have no real competing interests with each other. Russia should promise the restoration of the UK and the French Republic if the Third Internationale falls to appease the Entente. However, the Entente might lose their revanchist drive as the exiles grow older and they might turn inward if the exiles lose their influence. I also expect the Entente nations to join their resources into an ISAC joint nuclear program in the future.
Africa is an area of possible syndicalist expansion. With the German Empire greatly weakened and with the loss of much of their mainland territories, German control over Mittelafrika is sure to collapse due to independence and decolonization efforts. Syndicalism and communism might be very appealing to the oppressed Africans. Democracy is not likely going to flourish in Africa. Russia may need to send troops to support the new nations. Vietnam and Afghanistan like situations might happen in Africa.
The situation in the exiled Fourth French Republic (National France) will be very unstable. Even under a democratic National France, most of the native Algerians and other North Africans would not have the vote or equal rights. They will not stand for this situation much longer. Soon, the North Africans will make a violent bid for freedom which will be no doubt be supported by the syndicalists. The country will fall into severe instability. Either the French exiles will fruitlessly attempt to remain in power to the point of the collapse of the Fourth Republic and the French nationalists will end up exiled again to Canada. The other possibility is the Nationalists give in and give full rights to the whole native North African population. The French nature of the Republic would be diluted by the expanded voting franchise. Eventually the French Republic in exile might taiwanized into a giant French-flavored North African republic with little desire to reclaim the ”homeland” anymore. Same goes for the exiled Portuguese republic.
The Middle East will be a playground for syndicalist and Russian backstabbing. The Third Internationale would attempt to overthrow the monarchies of the Arab axis alliance in favor of socialist republics or at least friendly nationalistic dictatorships. Russia would do whatever it takes to maintain influence over the oil fields and keep access to the Suez canal.
The Americas were and will be again by dominated by the United States. Once America recovers from the Second American Civil War, they will reclaim their influence over Latin America. They will likely remain non-aligned or create a league of American states in the coming years. As long as Russia does not violate the Monroe Doctrine, the USA will be a valuable trade partner, an informal ally, and a vital bulwark against syndicalism in the Americas.
Of course, Kaiserreich might not have this events ingame because the devs have not developed many events for a post Second World War world yet so you may have to develop events yourself.