Plus if those Chechen rebels can get support from Georgia and Turkey, yeah, things will start looking up for them.
It's noted that Chechnya is majority Muslim, so it makes sense why other Muslim nations (Turkey for example is secular but majority Muslim, Iran and Afghanistan fucking hate Russia, and Azerbaijan is sadly Pro-Russian Government but a majority of its citizenry are anti-Russia) would support them if they were to rebel against Russia again. Georgia (and Armenia as well) is actually majority Christian, but Orthodox (and Orthodox Christianity actually has a more amicable history with Islam outside of the Byzantine Empire than Catholicism). Still, Georgia would absolutely support Chechnya in an effort for both countries to regain some Russian-occupied territory. Secondly, with Russia's majority of forces focused on Ukraine, and their supplies being strained even with that one front, a second front would be devastating to Russia. It would also be really fucking cool to see Mongolia shake off Russian influence and reconquer some of their ancestral lands.
*Dreams heavily of a Russian Federation collapse and instead Russia being broken up into several successor states.