Russia already sends gas to China via its Power of Siberia pipeline, which began pumping supplies in 2019, and by shipping liquefied natural gas (LNG). It exported 16.5 billion cubic metres (bcm) of gas to China in 2021.
[...]
Gazprom said in a statement it planned to increase gas exports to China to 48 bcm per year, including via a newly agreed pipeline that will deliver 10 bcm annually from Russia's Far East.

I may be wrong, but given that they also deliver LNG by rail, I don't think the non-interconnection between Siberian and Caucasian fields is a huge issue.

_{It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II}