Me being the TL writer I am (leaning strongly to the optimistic), I imagine the world beyond this being April 1996 being a "let's get this world back in one piece" over time.
In the short term, the Depression and the damage done to the Western countries will see them turn inward in a big way. This hurts Africa bad (likely intermittent famines in the 1997-1998 timeframe owing to food supply issues due to contamination) and stops China's rise in its tracks. Beijing's problems with Seoul, Tokyo and Vladivostok will very likely result in these three (and Taipei) joining forces in something of an informal anti-China grouping, with the Koreans and the Japanese burying the hatchets between them (and the FEK being the neutral negotiator between them) in the early 2000s as
@Sorairo commented on earlier in the TL. The FEK, for its part, steadily moves its identity to being the white-skinned Christians of Asia, which at first is seen as ridiculous by the other Asian nations but which rapidly becomes less and less ridiculous. Japan and Korea soon pair up with the FEK for natural resource access, leading to more than a few Koreans and Japanese in the FEK, with mines, energy developments and transport infrastructure improvements being financed in return for preferential access to these resources. The Trans-Siberian Railroad is re-established with Japanese and Korean rolling stock well into Siberia, giving the Siberians a large conduit for access to the world that doesn't go through the mess West of the Urals. Britain hangs on to Hong Kong, which China begrudgingly allows owing to a desire to not piss off the West any further - the events of April 1996 have tarred China's ruling party (for better or worse) with much of the same brush as the mad Stalinists under Anpilov, and Beijing soon has a real problem as the withdrawals into home markets by the North Americans, Europeans and other Asians alike cripples China's economic development. Beijing's government survives, but by the turn of the Century the West has made it clear that Beijing taking back Hong Kong and Taiwan is off the table, period, and having seen what the West was prepared to do in 1996, Beijing takes the warning seriously. In the further future, however, this works to China's benefit as they are able to develop their own technological and infrastructure improvements.
Hatred of a lot of Russian culture in the West after April 1996 is intense for several years, an order of magnitude beyond that showed towards Germans or Japanese during the World Wars. The Russians who came to the West as refugees are in fact the most hateful of all - most of them even before April 10-11, 1996 had little use for their past identity, and a massive wave of Russians changing their names to Western counterparts is a theme of the 1990s. Those with Ukrainian, Byelorussian or Caucasus backgrounds often shift their names in that direction instead, and with this the center of the Eastern world with the destructions of Moscow, St. Petersburg and almost all other Russian cities shifts decisively to Ukraine, with Kyiv, Kharkiv, Odessa and the cities along the Dnipro River becoming a hotbed of cultural remnants for those who lived through the madness to the East. With Western operations to secure Russia's remnants, the vast majority of surviving people of education head West to chase better opportunities - Sorairo touched on this, but I suspect it would be much beyond software engineers and the like. By the early 2000s, finding machinists, aircraft mechanics, civil engineers, aerospace designers and the like with Slavic accents but overtly-Western names is a very common occurrence, particularly in North America. Ukraine has begun its path that will lead it to becoming one of the most powerful nations in Europe by the middle of the 21st Century, and they do eventually re-establish their control over Crimea and areas along the Black Sea coast, to the immense benefit of those regions. Places with Ukrainian diasporas soon also grow Russian diasporas alongside them, particularly in Canada, the United States, Poland and Brazil (which have the largest Ukrainian diaspora populations), keeping the positive aspects of their culture alive while loudly dismissing the centuries of hatred and bitter pain that has resulted.
The West in recognition of what has been lost shifts dramatically to a Keynesian growth, re-establishing value-added industries in their countries and developing new infrastructure projects to put people back to work. Electronics manufacturing lost to Asia in the 1980s and 1990s shifts back to North America and Europe for both supply chain stability and political reasons, with Apple products regaining their "Designed and Made in California" labels by 1998-1999, for example. The loss of Russian oil and gas causes a massive energy crunch in Europe, leading to major investments in Western-friendly countries that can supply oil and gas, leading to major economic growth in Venezuela, Angola, Brazil and Nigeria, as well as everyone's money quickly repairing what was destroyed in Alberta, while electrified transportation grows to deal with the sudden and substantial rise in oil prices. The Middle East takes advantage of this in the short term, but the end of the decade the view of the West of Saudi Arabia and the Gulf States isn't much different than it is of some parts of the former USSR, creating a growth in synthetic petroleum development and some growth in nuclear energy in places that have enough willingness to expand on it after 4/10. Coal mines that produce harder grades of coal are reborn in numerous countries - Britain, Japan, Germany, Ukraine, Poland, Canada, the United States - for the sole purpose of supplying feedstock to synthetic petroleum plants, which use iron feedstocks to make synthetic diesel fuel as a direct result. Likewise, cellulosic ethanol is developed in the 2000s, the combination of this and synthetic crude (and oil shale dug out of the Powder River Basin) sees energy supply concerns slack off. Countless cities build electrified transit as job creation plans, and like the use of Art Deco and Streamline Moderne design was massively expanded in North America by the New Deal, postmodern, neo-futuristic and high-technology styles of design are massively expanded in the 1990s and 2000s by the projects to rebuild economies. While this obviously causes a major rise in the emissions of numerous countries, after the destruction of April 1996 there isn't that much concern.
Indeed, the destruction of Russia and the damage across large portions of the northern hemisphere from the nuclear blasts of 4/10/1996 ends up actually causing an unforeseen result for climate change, as the Mid-latitude cells are decisively disrupted by the war and the fires that result from it when combined with the two centuries of emissions into it from North America, Europe, the former USSR and East Asia causes a massive drop in the strength of the Mid-latitude Ferrel cells, resulting in the Hadley cells pushing northwards, dramatically expanding the rainfall in the horse latitudes. This also forces south, basically shifting the world's climate into something similar to the Holocene Wet Period, making the horse latitudes much wetter and somewhat warmer. Once-desert regions at these areas - western North America, the Sahel, southern Africa, Australia, much of Arabia, the Patagonia and Atacama deserts - suddenly have much more water, refilling endorheic basins in many places (including the Caspian and Aral Seas, Great Salt Lake, Lake Torrens, the Okavango Delta and the Qattara Depression) and counteracting melting polar ice in rising sea levels. This growth results in the 2000s being the decade of a major growth in food production, as many countries that were food-short suddenly weren't, and some that were already huge exporters (particularly Australia, Argentina, South Africa and the United States) saw their production increase dramatically.