As would be seen today, mainly socioculturally and demographically, a Russian empire that, for example, achieved "win" the first world war? What would your political culture look like and what would be its impact on the rest of the world?
ps: you choose the point of divergence as long as it remains after 1902
The possibilities are vast.
However, I'll tell you what it won't be: the Soviet Union.
The Russian Revolution was an enormous convulsion, as was WW1 itself, and without a Russian Revolution WW2 is also butterflied away or changed enormously. With the 3 defining events that shaped what would become the Soviet Union so very transformed, Russia will be very different. Don't apply expectations based on the OTL Soviet period onto a longer lived Russian empire.
I can tell you what else it won't be: the pre-1914 Russian empire! WW1, as mentioned above, had extreme effects on Russia even before the wheels came off in 1917. Depending on when the PoD is just in the 1914-1918 span, you could end up with wildly different outcomes from peasant socialist constitutional monarchy to liberal republic to tsarist Christian fundamentalism gone (even more) mad.
Some other fairly general points to keep in mind:
*Forced urbanization, mass death and education are all bad for population growth rates. The Soviet regime pushed all 3 in a big way. Further, Hitler killed alot of Russians. ALOT. On top of that, WW1 also killed alot of Russians. So on its own, no Bolshevik regime means a much higher Russian population. Add to that, if WW2 is butterflied or made less bad for Russia, that will also mean a much higher Russian population. Add to that, if the PoD results in a better WW1 for Russia or no WW1, then Russia has a much higher population. Of course, it is worth keeping in mind that significant credit for the post-revolution boom in literacy in Russia goes to foundations laid in tsarist times. So even without a revolution, Russia probably still becomes much more literate between 1920 and 1960. Avoiding the great demographic disasters and the Stalinist forced urbanization would mean that more literate population could be anywhere in a range from 500 million to over a billion by the modern day. Let that sink in for a moment. European Russia could be as densely populated as the Indian subcontinent (the two regions are about the same size).
*While tsarist Russia grew rapidly during the immediate pre-war period, so did most grain exporters - many of them struggled after the collapse of commodity prices in the Great Depression and experienced damaging political ructions (especially commodity exporters that like Russia in 1900 had poor literacy levels - low education and 20th Centuries marred by tyranny and bad decision making seem to go hand in hand). There's many reasons to think that a continued Tsarist regime would look more like a giant-sized Brazil or Argentina, not a giant-sized Japan.
*On the other hand, there's many reasons to think Russia would
not look like a giant-sized Argentina or Brazil. Russia would likely be a great power in most alternate 20th Centuries, if one with a population was poorer than other great powers, which means it would consistently have better bargaining power than the Latin American countries as it tried to navigate the many crises that are sure to face it. Further, while Russia's "vast resources" are very much an over-done trope (sheer distance pushing up transport costs, mineral and soil quality and climate all lead to many of the country's resources being uneconomical) it does have plenty of coal. And coal, along with education and population size, is one of the main things that differentiates countries that had a relatively successful 20th Century and those who are relative backwaters economically. (Even Japan, famous for being resource poor, became resource poor after using up those resources - it started the 20th Century with respectable coal reserves compared to most countries in the world, if low compared to most rich countries in the world.)
All in all, I would expect that a surviving Russian Empire would outperform the former Soviet Union by the present day, if only by virtue of avoiding the collapse the Soviet Union ran into. But that's not to say there aren't other paths to similar collapses, so maybe I am being over-optimistic. Nationalism - especially Russian nationalism - has the potential to push the empire into all-out collapse and one can argue that a continued Russian empire would be more vulnerable to that weakness than the Soviet Union was. Per capita incomes might thus be on par with those of modern Russia, but populations much higher and thus the state's power far greater. I would expect that a surviving Russian empire would be a significant food importer, since industrial agriculture, even if better implemented than it was under the Soviets, will struggle to output much more food than Soviet agriculture. Then again, it is possible to imagine a Russian Empire that follows a Japan-like industrial trajectory, meaning there is the wealth to employ technologies like polytunnels, glass houses and hydroponics at Neatherlands-level intensity.
Politically, in the 20s and 30s a continuing Tsarist regime is likely to be close to Japan (they had become close in the aftermath of the Russo-Japanese war, which helped the Russians get over some of the racist attitudes that led them into the war and realize that they and Japan had alot of common interests), to seek to expand into China, Turkey and Iran. In China, the northern half of Manchuria, Mongolia and Sinkiang could well end up being fully absorbed into the Russian empire unless China manages to be much more stable than OTL. Iran likely stays informally partitioned with the British until the Iranians are able to push the two out (possible if there's something like WW2) as neither power wanted to start a war for the other half. Turkey is very likely to end up a rump state and that rump state may end up becoming a Russian or a British protectorate. Depending on the PoD, Poland could be a semi-independent satellite or an autonomous region. Finland could also be either. Czechoslovakia is likely to be an ally of Russia. If WW1 ends with everything promised to Russia in OTL, possession of Constantinople greatly aids Russian trade. The rest of the gains are kinda irrelevant.
With a surviving Russian empire and a WW1, likely the peace is even harsher on Germany. If the French-Russian alliance survives (it may not, depending on how democratic Russia has become) they have the capability to contain the Germans even if the UK and US followed similar policies as OTL. Of course, France and Britain could have contained Germany easily in OTL, but as we see from our own history, capability doesn't mean people will use it.
Perhaps a surviving Russian empire means the colonial empires last longer, simply due to the lack of the Soviet example and the existence of the counter-example of a still very expansionist and imperialist Russia.
There's the possibility that all of this could lead to a better world, or it could be a mix of good and bad (for example, China could end up far worse off, but of course, it may escape anything close to the Maoist famines of OTL, so maybe it is better off overall even though it ends up more colonized by a Russo-Japanese team-up, on the other other hand, the Japanese and Russians have the capability to do some pretty awful things themselves. It could also just be worse. Even if Russia itself has a better 20th Century.
And there are so many black swan events that happen in real history. I would never have predicted anything as weird as 1930s Japan if all I had to go on is what the country looked like in 1913 and how WW1 effected it.
fasquardon