The man is phenomenally effective in certain engineering contexts and deserves to be listened to if he's talking about rocket engines or something. He's no more credible in public health and population modeling than any other rando.
A dwindling youth essentially enslaved to take care of a burgeoning aging population is pretty dystopian. So if life extension technology gets implemented with something like mRNA technology, then it seems like that would have to be balanced out by higher birthrates.
The population dynamics of such a situation would be dwarfed, imo, by the political and wealth inequality problems. Society is structured firmly around an average human lifespan.
Life extension in the sense of average lifespan marginally increasing is possible, but in the sense of reducing aging is a very very different problem.
Using the word "enslaved" will successfully paint anything as a dystopian future, that doesn't mean it is the inevitable path of mRNA vaccines. If we have life-extension technology, maybe people will start having more kids, maybe twins/triplets will become more common, maybe the poorest countries will never achieve the technology, nobody knows.
Maybe this puts some context around it. The first nuclear power plant came online in 1951. 70 years later, only 32 countries have nuclear power plants and the content of Africa has 2.
For me humanity is up for a massive shrinking. Either because we do it or (some decades later) mother earth does it.