(Cross-posted from the Wagner Group Rebellion Thread.)
I could think of a couple things that Beijing could (or more like, should) do in the face of present ongoing development in Russia, assuming Putin did not request for any significant help from China early on.
A - Based on the current situation:
#1 - Maintain communication channels open between Zhongnanhai and the Kremlin, plus between the August 1st Building and the Russian Defense Ministry Building;
#2 - Offers a neutral ground for both Moscow and Wagner to conduct negotiations in order to settle their disputes, with Beijing acting as the middleman;
#3 - Making sure that Chinese citizens currently in Russia be on constant alert for any happenings through the PRC Embassy in Moscow, and be prepared to conduct evacuation missions of Chinese citizens from Russia;
#4 - Upgrade the Combat Readiness Condition (CRC, 战备等级)* of the People's Liberation Army (PLA), People's Armed Police (PAP) and the Militia to Level 2 (Training) for the Northern and Western Theater Commands, and Level 3 (Mobilization) for other Theater Commands; and
#5 - Request a meeting at the United Nations Security Council (UNSC) to discuss on the present situation in Russia.
B - When the prospects of large-scale disorder or civil war becomes increasingly likely/worsening in Russia:
#1 - Launch evacuation missions to ferry Chinese citizens out of Russia ASAP, especially those living in and around affected areas of tension or conflict (thank goodness China can mass-produce the Y-20Bs now).
#2 - Initiate direct channels of communication with the other heads of states, heads of governments and supranational organizations, especially with P5 members (Washington DC, Moscow, Paris and London) and others (New Delhi, Brasilia, Tokyo, Jakarta, Ankara, Brussels and Addis Ababa) to permit swift communication and coordination in case of worsening crisis in Russia;
#3 - Upgrade the CRC of the PLA, PAP and the Militia to Level 1 (Combat Ready) for the Northern and Western Theater Commands, and Level 2 (Training) for other Theater Commands;
#4 - Orders the PLA, PAP and Militia who are stationed along and around the China-Russia and China-Mongolia border regions to go on full alert for any unusual or hostile behaviors by the armed forces and armed elements of Russia;
#5 - Set up plans for the entire country to enter wartime mode across most economic, industrial and societal sectors of China;
#6 - Enact contingency plans for establishing and maintaining the stability and security of Siberia and the Russian Far East through the means of political, military, or a combination of both;
#7 - Enact contingency plans to secure the strategic assets of the Russian armed forces (strategic bombers, SSNs, SSBNs, mobile TELs and missile silos) and the Russia nuclear arsenal;
#8 - Continue offering a neutral ground for both Moscow and Wagner to conduct negotiations in order to settle their disputes, with Beijing acting as the middleman; and
#9 - Continue request urgent meetings at the United Nations Security Council (UNSC) to discuss on the evolving situation in Russia, formulate resolutions, and/or setting up UN-directed peacekeeping efforts that can enter Russia to conduct peacekeeping missions.
C- When sh1t REALLY hits the fan, i.e. full-scale, all-out civil war breaks out between rivalling factions of the armed forces and armed elements of Russia:
#1 - Upgrade the CRC of the PLA, PAP and the Militia to Level 1 (Combat Ready) for all Theater Commands;
#2 - Launch the plans that would transform the entire country into entering wartime mode across most economic, industrial and societal sectors of China;
#3 - Maintain direct channels of communication with the other heads of states, heads of governments and supranational organizations, especially with P5 members (Washington DC, Moscow, Paris and London) and others (New Delhi, Brasilia, Tokyo, Jakarta, Ankara, Brussels and Addis Ababa) in preparation for any worst-case scenario in Russia;
#4 - Continue offering a neutral ground for both Moscow and Wagner to conduct negotiations in order to settle their disputes, with Beijing acting as the middleman;
#5 - If the situation permits and UN support can be expected, provide support for UN-directed efforts to enter Russia to conduct peacekeeping missions;
#6 - If the situation permits and UN support cannot be expected, launch contingency plans to send PLA expeditionary forces into the regions of Siberia and Russian Far East in order to conduct peacekeeping missions, plus establishing & maintaining the stability and security of the region, preferably with the support of at least some armed elements and local governance of Russia in the region;
#7 - If the situation across Russia becomes gravely threatening towards the national security and national interests of China and the Chinese people, launch contingency plans to militarily invade and occupy the regions of Siberia and Russian Far East in order to prevent spillovers across the China-Russia and China-Mongolia borders;
#8 - Be prepared to provide humanitarian aid and support for waves of Russian war refugees crossing the China-Russia and China-Mongolia borders;
#9 - Launch amnesty programs targeting Russian military personnel in order to persuade them towards defecting by voluntarily flying their warplanes, driving their tanks or sailing their warships to Chinese-controlled air bases, Chinese-controlled border checkpoints and Chinese-controlled naval bases for safekeep;
#10 - Launch contingency plans to secure the strategic assets of the Russian armed forces (strategic bombers, SSNs, SSBNs, mobile TELs and missile silos) through the means of: 1. Voluntary handing-over of the assets to the PLA by the armed elements of Russia; 2. Infiltration of Chinese special forces to gain control of the assets; 3. Launching attacks against any armed elements that refuses to do so in order to gain control of the assets; or 4. Disable/destroy those assets if attempts at gaining physical control of the assets is deemed not viable;
#11 - Launch contingency plans to secure the Russian nuclear arsenal in order to prevent nuclear warheads from falling into the hands of extremists and terrorists, either through voluntary means (refer #6) or involuntary means (refer #9); and
#12 - Continue evacuation missions to evacuate any remaining Chinese citizens still in Russia whenever situation permits.
*CRC is the Chinese equivalent of the US DEFCON.
End of my random, incoherent and less-than-knowledgeable ramblings.