1st Celestial Empire + 3rd Rome = ?
The relations between the "Celestial Empire" and Russia, which is twice the size of China (9.6 million km²) but has only one-tenth its population (1.4 million) and GDP (19.9 trillion), have always been quite complicated, to say the least.
On the one hand, the history of Sino-Russia relations consists of open military confrontations, such as the Manza War in 1868 or clashes near Zhenbao (Damansky) Island in 1969, as well as smaller, ever-lasting border disputes "settled" in multiple treaties such as the Treaty of Kyakhta (1729) or the Treaty of Peking (1860), which assigned Outer Manchuria (Primorskiy Kray) to Russia. On the other hand, there have been a number of "eternal" alliances, such as the Li-Lobanov Treaty (1896), or famously, the "China-Soviet Union: Treaty of Friendship and Alliance" (1947).
The historically latest surge of camaraderie in the 1940s was abruptly replaced, first by the Sino-Soviet Split in the 1960s and later, after President Nixon's visit to Beijing in 1972, by open geopolitical rivalry in the 1980s.
Both Russian and Chinese politics are highly personalized, so typically there is a span of 20-25 years, which is the average length of stay in power for political figureheads in those countries, between periods of hostility and friendship. It seems that the current Putin-Xi "rapprochement" may also endure for a prolonged period of time, considering Xi came to power in 2012.
Historical evidence demonstrates that the highly emotional political rhetoric that is typical at the beginning of these periods does not usually result in prolonged wars or economic and social amalgamation. These two countries have always been too distant from each other in terms of ethnicity, culture, society, economy, and politics to make this alliance stable. It is mostly based on "against" premises rather than "for". The earlier Russo-China friendship was "against Britain" and then "against Japan," while the current one is "against the USA" once again.
On a practical note, however, neither China's export of consumer goods to Russia (USD 38 billion in 2021) would be able to replace its 10-fold exports to the USA (USD 365 billion in the same year), nor Russia's natural gas supply to China (22 billion cubic meters in 2021, with a maximum increased capacity of up to 38 billion cubic meters in 2025) would be able to replace Russian gas exports to Europe (around 140 billion cubic meters of gas or about 68 billion US dollars in 2021).
More consequential is the potential for military cooperation between China and Russia. For example, Russia's tank manufacturing capacity is estimated to be around 1,000 tanks per year, with about 17K tanks in reserve (with 3-4K in a "battle ready" state). Theoretically, this could be complemented by comparable Chinese tank's productions (exact numbers of tanks produced each year in China are unknown).
Additionally, China reportedly holds at least 8K tanks in reserve part of which could potentially be sold to Moscow. However, it must be added that almost all of these tanks are of the old, post-World War II generation with weak armor and reduced communication/electronic capabilities. With about 3,000 tanks incapacitated by the Ukrainian army each year, almost doubling Russia's heavily armed machinery forces could substantially prolong the ongoing war in Europe.
Overall, however, the closeness between Xi and Putin has the potential to strengthen Russia both economically and militarily in the short to medium term.