Military formations drawn from across Russia are currently bearing the brunt of Ukraine’s counter offensive.
In Zaporizhzhia Oblast, the 58th Combined Arms Army is defending heavily entrenched lines; normally it secures Russia’s volatile Caucasus region. Around Velyka Novosilka, the 5th Combined Arms Army and Naval Infantry hold the front; they are routinely based 7000km away as a balance to Chinese power.
Around Bakhmut, the defence is now largely formed around airborne regiments normally stationed in western Russia, who normally act as an elite rapid reaction force in case of tensions with NATO. The way Russia is accepting risks across Eurasia highlights how the war has dislocated Russia’s established national strategy.
I wouldn't call it "need to back" Russia, but preventing China from getting stronger and taking territory by force is something we don't want them to make a habit of. And arming Russia against China would have a similar effect as arming Ukraine against China: super cheap for the West and the main adversary gets weakened.
Russia had to let go of Ukraine first, though.