This is rather similar topic: why did not Indonesians colonize Australia?
Like Qing had manpower and tools but looks like they did not have a political will. This is rather strange that Russians simply expanded into wasteland without little local and Qing intervene. I quess the the best question is, why was Russia politically motivated to colonize Siberia and Qing had not?
Siberia was complitely open to Qing. They had defeated hordes and annexed them. They had no enemies and their nation was isolated but stable. Qing simply had every opportunity to colonize Siberia but decided not to do that.
Siberia is a horrendous place. It's an enormous trackless wilderness full of biting insects, disease and impassible terrain. The climate is truly awful in a way that no other part of the northern hemisphere is, you have places where the yearly temperature range exceeds 100 degrees. It is so bad that the climate actually gets better as you approach the arctic circle. In most of Siberia anything approaching agriculture is impossible. Siberia might look beautiful and wild but this is not some Appalachian frontier of opportunity. Before some very, very brave men developed a network of long-distance railways, the only way to get about Siberia reliably was by sailing along rivers and occasionally dragging your ship over dry land. Even today, the only part of Siberia that is colonised by large populations of human beings is the narrow southern belt that forms the edge of the steppe.
Siberia might have been 'open' to the Qings in terms of politics, after all this was a place only guarded by small bands of Russian Cossacks. The Manchus did war with the Cossacks and they managed to keep the Chinese frontier intact (for a while at least), and they managed to hold on to much of that steppe frontier land in northern Manchurian and Mongolia. But there was absolutely no reason to go further north than that. Siberian resources could be accessed via trade with the small Russian population that lived in the south, there was no reason for Chinese colonists to go and try and seek out new lands there, and marching an army of any size into Siberia is a good way to lose your entire army.
Russian colonists moved through Siberia via river.
If you're going from the west you can access this network relatively easily: you can sail there from Arkhangelsk or further west, you can cross the Urals and enter western Siberia which has a relatively large population and a better climate (it was home to the Sibir Khanate at one point), and from there you can use the Yenisei-Lena portage to get around the impassible ice at the Timur peninsula. Essentially you can bring your boat all the way from the heart of Russia to the Pacific.
From the east your options are much more limited.
Unlike in Russia, you can't make a few relatively easy and familiar jumps to access the rivers. You have mountain ranges and hills barring the way, you have the vast wastes of Mongolia, you have the mountains of northern Manchuria, and the nearest estuaries are thousands of miles along the coast from China's great rivers and ports. Yes the northern border of the Qing Empire did pass near a lot of those navigable rivers, but that's the northernmost frontier, miles from any big population centres.
So, to sum up:
1. There were few reasons for the Qing to try to reach Siberia or colonise it.
2. Geographically Russia had a big advantage over China when it came to accessing and exploring Siberia.