Robotics is catching up to AI. Loads of money is being poured in to improving both of those things, because in order to replace manual human labor they both need to work together.

We're talking about the people who own or run massive companies, with an emphasis on tech sector people focusing R&D on robotics, AI and automation. There are places testing new versions of these things all the time.

And a global pandemic that causes humans to quickly fall sick and die is definitely going to result in infrastructure damage, but odds are it will be mostly vandalism and looting. People would be scared, desperate, and trying to stay alive, they wouldn't be focused on getting together to smash factories and supply chains so that infrastructure can't be used after they die.

As for genetic diversity, I don't honestly think they're making detailedp lans for a century or two for now, but it's possible. There are loads of fertility clinics with eggs and sperm frozen from healthy donors throughout the world already. I saw a story recently where an embryo that had been fertilized over 30 years ago and then frozen was successfully implanted and the baby born healthy.

Plus it's unlikely they wouldn't want a decent number of people to survive throughout the world. It's not nearly as much fun being rich and powerful and part of a small cabal fully controlling the world without servants and lessers to feel superior to, and have to menial or necessary tasks, and torture and rape and all that jazz. If someone funded the creation of a virus like this, along with a cure or innoculation that would keep people from catching it, and they were securely watching what was happening to the world from their comfy bunker... again, tech moguls. It wouldn't be difficult to set up hidden caches of the cure, or even have a signal that would cause fleets of drones to distribute it along with directions for taking it to enough places in the world that enough humans would survive to make survival of the species long term pretty secure while keeping the survivors in small enough groups with enough distance between them to make it very unlikely for an unmanageable number of them to decide to form a mob and hunt down anyone they find in a bunker.

For the rest... solving complex manufacturing, food, medicine, all of it are things genuinely being researched at many well funded places in the world. AI and robotics is the likely thing that will take care of the bulk of it. If you want to go full conspiracy nut you could consider the possibility that all or most of the embarrassing public failures of robots that have been news lately making big companies look stupid were staged entirely to keep people from believing robotics was anywhere near being able to replace us like the dumb billionaires with all their stupid think tanks and NDA secrecy spending trillions on it expect it to.

There are also patents and research into things like 3D printers for chemicals/medicine. Large tanks of hundreds of chemicals needed, the conditions needed for each reaction programmed and monitored, each reaction done in the proper succession to get the desired result someone picked off a menu. I haven't seen anything that would indicate loads of progress... but it's not exactly like Eli Lily and Merck explain how everything they make is done or what they're researching to me. :p

Like... I get it. This sounds like crazy shit. It's a crazy idea. But with the advances in technlogy, financial control, lack of genuine public oversight... it's all pants shittingly terrifyingly possible. Of course there would be a chance it would all go horribly wrong somewhere along the line. But they're also asshats who own prediction markets and make billion/trillion dollar bets on things that could possibly go horribly wrong somehow already.

10% chance humanity pretty much ends.... 90% chance you and your family and kids become virtual Gods on earth, with endless unchallenged access to whatever you want and complete control over the systems that create and maintain everything and the lives of all the little toy humans, able to kill nearly any other human and any animal (or species!) you want. I really don't think anyone should have the power and finances to set that sort of button up, but people do, and they're not the sort of people I'd ever trust to not push it.

(This long, rambling response sponsored by changing ADHD meds yesterday morning. ^^)