Putin would be a fool not to capitalise on anit-chinese sentiment in africa limiting their recovery aid soft power projection, if he has the wherewithal. His troll farms should already be looking to get trump back in in a big way; the crisis will drive even more eyeballs to social networks as their most trusted news source over there just like they did in syria in 2012. It might be a moot point if he's really controlling infection domestically or only appearing to, his old enemy to the west is severely weakened and will continue to lack the necessary paranoia to parry him while they try to "be better humans". He played Erdogan well, and that won't stop now.
I think he can like Xi plenty, but that won't stop him seeing a China with independent access to resources in africa and no need for old Vlad as a threat, and much too close for comfort. If they can't forge an alliance (both leaders for life now), the knives will come out. India will try and profit, but with too regional a scope. If the US becomes truly irrelevant south america becomes the next proxy battlefield for them, if europe and brazil don't adapt quickly enough. That's another reason for china to pursue good patronage networks in oceania, as they currently are doing.