From a previous answer I wrote, with some editing:

As far as Russia east of the Urals goes, this area is not that underdeveloped. Four of Russia's ten largest cities are located there: Yekaterinburg and Chelyabinsk in the Urals region and Omsk and Novosibirsk in Siberia. These areas are significant grain-producing regions, especially Western Siberia. Starting in the 1930s, the Urals and Siberian regions also saw major industrial development, starting with the 1929 Five Year Plan and accelerating during World War II. Uralmash in Yekaterinburg (then-Sverdlovsk) was a major tank producer for the Soviet war effort in 1941-1945, and the "Kuzbas" (Kuznetsk Basin) in Siberia is a major coal producing and metallurgical region.

So the question is less why are those particular parts of the Urals and Siberian regions developed, and more why do the settled, economically productive regions suddenly stop.

I hesitate to give one simple answer why these areas were underdeveloped, but one item that I would point to that poses a particular challenge and that might get overlooked is permafrost. Once you get beyond Western Siberia, the rest of the Siberian and almost all of the Far Eastern regions are completely within a zone of continuous permafrost that stretches from the Arctic Ocean coast into northern Mongolia (and technically continues into the Tibetan Plateau). In comparison, the area covered by permafrost in North America is much smaller in absolute and relative terms.

Building (roads, railways, towns, you name it) in this area is exceptionally challenging. There is an "active layer" over the continuous permafrost that melts and freezes with changes in temperatures - this can cause conditions such as "frost heave" and uneven melting and freezing that move the ground and cause damage to buildings, bridges, roads and pipelines. Those very structures themselves can generate heat that contributes to the problem. In spring and summer, the layer of permafrost also means that plants can only put down relatively shallow roots, and that meltwater often stays undrained at and near the surface in very swampy conditions. Before steamships were used, for example, it was often easier to travel on major Siberian rivers such as the Ob, Yenisei and Lena in the winter when they were frozen, rather than trying to traverse swampy regions around the thawed rivers.

Which is not to say that these regions were not colonized, just that they were done at great financial and human cost. The settlements that proved most profitable in these regions tended to be mines, such as Norilsk (which means metals such as nickel and copper), and the Kolyma region, which produced gold. Both of these areas were originally developed with the significant use of forced labor from camps in the 1920s and 1930s, with the Kolyma gold mines and fields being under the jurisdiction of "Dalstroy", which was probably one of the only actually profitable portions of the Stalin-era forced labor system.

So, in short, in addition to a severe climate, the challenging nature of building settlements in permafrost areas meant that only areas that had strong strategic or economic value tended to get developed, and even then at great expense. Finally, it's worth noting that developing infrastructure in this region can be challenging enough, but this infrastructure needs very high levels of maintenance to remain usable. An infamous example of the adverse effects of neglecting this would be with the Baikal-Amur Mainline, which was a railway further north of the Trans-Siberian (and thus further away from the border), which was announced and build with great fanfare (and great expense) during the Brezhnev years. However, even after its construction, it has been heavily underutilized and required extensive reconstruction just to keep portions of it in service.

A current add-on: another historic process I would note is the tendency of Russia to try to push south, and succeeding to varying degrees depending on how strong its southern neighbors have been. So the area around Amur and current-day Vladivostok had been off limits to Russians ever since the 1689 Treaty of Nerchinsk with the Qing, and this held until those regions were annexed by Russia in 1858. Even after this time, Russia preferred to run the Trans-Siberian Railway through Manchuria to Vladivostok (and also to Port Arthur aka part of modern-day Dalian) rather than through Russian territory. The current line on Soviet/Russian territory was only built in 1930. So the general thrust of development has always gone southwards rather than northeastwards, largely for the reasons mentioned above.