A population of 10 million is the population of England circa 1812. Machine tools, glass optics. Electricity should be possible. Powered flight, if you had hydrocarbons.
Oil would be a problem. All the easy deposits are tapped. A successor civilization would have a hard time progressing past steam power.
A lot depends on how we crash to 10 million. If all the wells are shut down cleanly, thoroughly documented, then the people blink out existence, then the 10 million could live quite a white just on today's reserves. If we end up at 10 million after decades or centuries of warfare, then there won't be any oil left. (Plus the sea would be a lot higher, and many oil deposits would be in places where summer temperatures would be fatal for humans) Liquid fuels can be made from steam cracking of coal hydrocarbons, but they're expensive.
No nuclear power, no turbines, none of the exotic metals that require electron-beam vacuum furnaces. No pharmaceuticals, no long supply lines, limited manufacturing specialization or economies of scale. Fasteners would be expensive again. Fabric would be expensive. Probably the number one most important thing to get working again is production of artificial fertilizers. Without that you're stuck with organic agriculture and 1 out of 2 people working in the fields.
And somehow I get ten sentences into this comment before remembering about a book I read that made the exact same point about fertilizer: https://www.amazon.com/Knowledge-Rebuild-Civilization-Afterm...
https://www.amazon.com/Knowledge-Rebuild-Civilization-Afterm...
Also at the talk were Vinay Gupta (Ethereum), Rosalind Eggo, and Hugh Lewis discussing different avenues to potential Apocalypse and their likelihood, etc.
[0] https://www.youtube.com/watch?v=FPxBhqonZEQ
[1] https://www.amazon.com/Knowledge-Rebuild-Civilization-Afterm...
Here are some books I've given as gifts recently:
* The Knowledge: How to Rebuild Civilization in the Aftermath of a Cataclysm, Lewis Dartnell[1]
* The Black Swan, Nassim Taleb[2]
* Siddhartha, Hermann Hesse[3]
* The Happiness Trap, Russ Harris and Steven Hayes[4]
* Code, Charles Petzold[5]
[1] https://www.amazon.com/Knowledge-Rebuild-Civilization-Afterm...
[2] https://www.amazon.com/Black-Swan-Improbable-Robustness-Frag...
[3] https://www.amazon.com/Siddhartha-Hermann-Hesse/dp/161382378...
[4] https://www.amazon.com/Happiness-Trap-Struggling-Start-Livin...
[5] https://www.amazon.com/Code-Language-Computer-Hardware-Softw...
https://www.amazon.co.uk/Knowledge-Rebuild-Civilization-Afte...