IOTL, there were some Russian penetrations into Siberia. Some Russians - mainly Cossacks - had dreams of annexing large parts of Siberia, or even conquering the whole of it. Of course, these dreams never came to pass. But suppose they had? What if Russia had been able to take control of Siberia?
Well, there was nothing of value (as known prior to the XX century) to the East of Ural Mountains and strictly speaking Russia got some territories East of the mountains with a border on Ob - Yirtish line which provided a sensible secure perimeter. Penetration further to the East is an interesting idea but it does not look too practical by a number of reasons:
1st, most of the territory (I assume that "Siberia" is used in a vernacular meaning) is uninhabitable: it is either deep forest (taiga) or permafrost.
2nd, Russia never had excess of a population allowing a meaningful migration to the areas which could be of some usefulness.
3rd, the distances would make communications prohibitively long: travel from Ural to the Pacific would take a couple of years, taking into an account a need to wait for the major rivers to freeze, etc. How these travelers would be supplied is another big question.
4th, what's the end game? Let's assume, just for the argument sake, that the Russians got it all the way to the Pacific coast where some reasonably good lands are available and even built some ports. Then what? There is nobody to trade with over the sea/ocean until the late XIX and you could easily get tea and silk from China either through the Bukhara merchants or directly across the OTL border (admittedly, there is some not quite "pacified" by the Chinese area between Yirtish and Baikal Lake but the natives were routinely bought to guarantee caravans' safety). A lot of expenses with no tangible gain.
5th, if you do all that Pacific thingy, you are bound to build and maintain at least some navy here and the same goes for the troops to provide security initially against the Chinese and later against Japan, USA, Brits and whoever else. Again, a lot of expenses and strategic vulnerability to which end?
6th, in the late XIX - early XX there is finally a technical possibility to improve communications by building a railroad all the way to the Pacific Coast. A huge effort and expense would negatively impact an ability to build the railroads in more populated regions, including the railroads which would have a strategic importance in the case of a war. And in the case of a military conflict with China or Japan this road would not have enough of a carrying capacity to provide an adequate flow of troops and supplies. Not to mention that whatever fleet you have on the Pacific would be just one of the fleets that you have to maintain while any of your opponents would be able to concentrate its whole navy against you.