China's geostrategic objectives are centered around three main objectives, 1. securing energy and trade flows to China by keeping global naval corridors and trade routes open, and long term creating Chinese controlled alternatives to those (BRI), 2. creating strategic depth+deterrence around China vs US+allies (eg. first step securing 9 Dash line) and 3. securing access to vital resources in and around China through diplomatic means.
In Chinese policy papers the area north of Manchuria/Dongbei has low priority and only gets talked about in the hypothetical case of a Russian collapse. In that scenario the Chinese would make a landgrab north to secure the border area, create strategic depth and secure (future) Arctic shipping lanes and access to hydrocarbon resources. Yet Russia isn't going to collapse because it's not in the US interests to see Russia collapse, Russia has it's role in keeping the Franco-Germans busy & US dependent and seeing Russia devolve into warlordism with 8000 nukes in between is not to the benefit of DC.
The only people that talk about the Far East as legitimate Chang clay is the online nationalist crowd. This is a relatively large yet powerless fringe group which was nurtured as a dialectical Ersatz ideology after the 1989 Tiananmen Protests and the subsequent soul-searching of the CCP ideologues. The e-nationalists are fueled by historic revanchism and their territorial claims are rooted in recent history, large parts of the Russian Far East were part of the Qing Empire in the late 19th century.
Chinese nationalists/irredentists consider the 1689 Treaty of Nerchinsk to be the legitimate Chinese- Russian border. In 1858 (Treaty of Aigun), 1860 (Treaty of Beijing) and 1864 (Treaty of Tarbagatai) the Qing ceded large parts of Qing Empire territory to the Russian Empire after a series of military defeats, and the border was established at the Amur River. In modern Russia these territories include Tuva, Sakhalin Island, the Jewish Autonomous Region, Primorsky, Amur and Khabarovsk.
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Chinese nationalists have been sidelined since long. After the anti Japan riots (2005-2012, Senkaku Islands, Yasukuni Shrine, JDF rearmament etc) and their increasingly belligerent and demanding rhetoric the nationalists standing got tarnished, low key support withdrawn, and the movement relegated to the fringes. CCP top dogs became uneasy with the antics and vibe, the large, high energy and often violent public gatherings of tens of thousands of young men scared the potbellied hairdyed CCP dinos, so the problem was solved before it could grow. Not in line with the 'Harmonious Society'. Currently the nationalists only exist in the online sphere where they blare their slogans all day long yet are smart enough to refrain from criticizing the Party.
Shanghai comedian Zhou Libo posted this map last year, was censored by the CCP propaganda arm.
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As if everyone didn't know that already.