More specifically from the fall of the Sibir Khanate right up to the start of World War One.
So the story or Russian expansion into Siberia is first very slowly then slightly all at once. Before nationalism started to take shape as a recognisable ideology in the early 19th century there was little political or economic impetus for the Russian state to try and expand into Siberia. When expansion started in the late 16th century it came in the form of an informal network of traders based around the rivers of Inner Siberia. For most of this period the only remotely valuable good to be had in Siberia was fur, with mineral reserves being unknown or inaccessible.
As a result settlements were small and inhabited by traders rather than families, existing to facilitate the fur trade rather than as tools of the state. When more organised actual conquests happened they were organised along these lines, with the attacks of Yermak being done in the interest of nobles who stood to gain from the fur trade. These created an environment where Russians established tributary relationships with Siberians, demanding fur in return for being mostly left alone.
Russia in this period was much more concerned with its Western rather than Eastern affairs. With threats such as Sweden, Poland, and the Ottomans dominating Russian government rather than the empty and largely unthreatening Siberian wastes. When threats occurred they were from nomads who could normally be bought. Resistance to Russian rule was therefore pretty nonexistent, with the poverty and sheer lack of people making expansion easy.
This did start to change later on, Russian and Chinese interests bumped up against each other, resulting in a few skirmishes, but neither side wanted to or was logistically capable of waging a war in Siberia so they agreed to carve up the area. In the 1800s Russia reneged on this, pressing hard into China’s sphere of influence due to their desire for a warm water port on the Pacific. This led to the construction of the Trans-Siberian railway and saw much higher state investment in the region. This railway produced the logistical capacity for large settlements and eventually cities to emerge in the somewhat fertile band that runs across the length of Southern Siberia, where the railway was built.
Follow up question: was there any Russian motivation for their acquisition of Alaska beyond "we need all unclaimed land we can get"? Because I just think it's interesting how, after tripling the size of their already massive empire with wild frozen taiga, they reach the Bering Strait, see more of the same topography as Siberia, and still think they should cross the ocean and continue so far from Europe just for more harsh wilderness
Any books on this topic?