I think it's much easier to talk of "Russian" architecture when one is discussing the work done by and for the classes below the senior aristocracy and monarchy. Once one takes the Middle and Far East out of the equation (at least for the most part), most great architectural movements that have affected the edifices put up at the top of the social structure in Russia and elsewhere have been transnational.
Ivan III and Ivan IV brought in architects and builders from western Europe and, while their work looks "Russian" to modern eyes, it introduced distinctly non-Russian design and materials. The Palace of Facets, which is viewed by many as an example of Old Russian architecture, for example, was put up by a European architect and could have fit quite nicely into the cityscape of Renaissance Florence. European Romanesque architecture, which evolved into Gothic architecture, drew primary influences from Byzantium. Northwestern Europe's neoclassicism was based on Greek and Roman forms which, in the first period, were far more prevalent in Asia Minor, North Africa, and the Near East than they were in western Europe. Europe was overtaken by a rage for Egyptian forms as a result of Napoleon's late-18th-century expedition to Egypt, and those forms acquired a new lease on life with the 20th century's Art Deco movement. Then there were the enduring European fads for Chinoiserie and, later, Japanese art forms. (Some of Josiah Spode's most famous early 19th-century ceramic patterns carried adaptations of Japanese imari decoration, and Frank Lloyd Wright's arts and craft work and the associated decorative arts were heavily influenced by Japan.) At the top levels of wealth and society, it becomes very difficult to talk about a "national" architecture, unless referring to a period in which a nation undertakes a self-conscious reversion to what it thinks were its earlier indigenous forms, such as happened with the Pan-slavism and Russification movements that began with Alexander III.
Also, beginning with Catherine the Great, Russian monarchs were themselves progressively less Russian. It has been calculated that Nicholas II was 1/80 Russian by blood, as all his predecessors from Catherine II onward either were western Europeans or married western Europeans. They tended to think of themselves as Russians and European, every bit as much as a Hapsburg thought of himself as Austrian and European.
So I would argue that Russian architecture -- at least imperial and aristocratic architecture -- did not "copy for localization" anything any more than did English, French, German, Italian, or Austrian architecture. Every one of these countries was rife with buildings that were in the central flow of transnational movements with origins from all over the world. If Rastrelli's work in St. Petersburg was a Russianized "copy" of anything, then Palladio's work in Italy was a modernized "copy" of early classical forms. If Quarenghi's work in Russia was a Russianized "copy" of anything, then Wren's work in London was an Anglicized "copy" of French architecture and Italian (especially Bernini's) architecture. If Cameron's work at Tsarskoye Selo was a "copy" of anything, then one would also have to speak of Adams' work at Syon House in London as a copy of Pompeii.
In short, I do not think Russia copied anything in architecture. I think that, as it unified under Ivan III and began to think more and more of itself as a member of an international community, it eventually joined the other European powers in drawing from the same transnational movements from which they drew for their architecture.
