I caught this a little late, but you pose a quite interesting question: starting from Fathers and Sons (published 1862, but discussing the environment of the 1830s onward), What is to be Done? was published the following year, and Notes from the Underground was published in turn in 1864. Dostoevsky returned to these themes in Demons and to some degree in The Adolescent. So all of this is happening over a very short and politically charged time; the liberal agitation for the abolition of serfdom was realized in 1861, and it seemed that indeed further liberalization was on the way. These somewhat anemic measures, as they were perceived by Marxists, anarchists, and other radical elements, simply preserved and modified the ancien regime: thrusting state-owned serfs into subsistence-farming or, later, factory work hardly resolved the economic inequality of the Empire. At any rate, the summer of 1862 was marked by violent student uprisings, and the following winter saw the attempted Polish January Uprising.

Additionally, it was the liberalization under Alexander II that even allowed for these works to be published as they were. Fathers and Sons explores nihilism, which is a rather complicated and evasive position; many self-professed Russian nihilists held to deeply divergent views. The central tenets are rejection of the extant structures: serfdom, monarchy, Orthodoxy, and so on. For some this meant terrorism or suicide, for others the absence of political commitments. Bazarov, for example, initially believes that love is incompatible with his nihilist beliefs.

This is what Chernyshevsky rejected in What is to be Done?: instead one must have political commitments. The fictional veneer for Chernyshevsky is thinner than in Dostoyevsky or Turgenev, and the novel very much plays the part of a philosophical treatise. To turn to Dostoevsky, he held nationalist, Slavophilic views, ones inherently at odds with the radicalism of Chernyshevsky. In perhaps the most famous vignette of Notes from the Underground, he derides at length the utopian Crystal Palace for denying individuality and freedom:

All human actions will then, of course, be tabulated according to these laws, mathematically, like tables of logarithms up to 108,000, and entered in an index; or, better still, there would be published certain edifying works of the nature of encyclopedic lexicons, in which everything will be so clearly calculated and explained that there will be no more incidents or adventures in the world...What has made them conceive that man must want a rationally advantageous choice? What man wants is simply INDEPENDENT choice, whatever that independence may cost and wherever it may lead.

(Schopenhauer returns to this theme, as "a ship without ballast is unstable and will not go straight")

To most directly respond to your question, I will defer to the Slavicist Sasha Murphy on 19th century Russian literature:

The significance of literature in Russia was different from that in Western Europe. Whereas in Europe professional academics shaped professional academics of Europe were in Russia replaced by non-academics who acted as society’s original and influential thinkers.8 Up until the twentieth century, the majority of Russian thinkers were not professors, but literary critics. The term ‘literature’ in Russia has been conceived very broadly, not just to include the novel, poetry, and short stories, but also political and philosophical commentary. Russian novelists were political, social, and cultural critics as well as literary critics. In Russia, more than anywhere else, writers have concerned themselves with the perennial ‘problems of man.’ Literature of this period challenged old beliefs and sought new ones; it came to work for society by working against it. Literature acted as a forum for political discussion as the more obvious government channels remained closed within Russia.

One reason you're finding more philosophical novels in Russia than elsewhere is the fractured political environment of the 1840s onward, without more traditional outlets; and the enmeshment of philosophical questions with political ones (note these aren't especially cerebral concerns, but urgent ones on the place of future of Russia itself). These themes were taken up by various other authors, like Mikhail Artsybashev in Sanin or Nikolai Leskov's Daggers Dawn, but they aren't the direct replies like we see earlier. Anti-nihilistic novels and short stories were quite common in the 1880s under the direction of the conservative editor Mikhail Katkov, and while these were quite popular they largely aren't very good as literature.

But I don't think that philosophical novels, or novels as the chief venue of a philosophy, are uniquely Russian. Compare Being and Nothingness with Nausea, for example. One is overtly a philosophical work, but I don't think that means the other is necessarily relegated to "conveying a philosophy" but not itself acting as a treatise on that philosophy.

Murphy, Sasha. "The Debate around Nihilism in 1860s Russian Literature". Slovo 28:2 (Spring 2016).