If you’re looking for a number, I don’t think anyone can give you something reliable, because the important factors involved here are constantly changing.

What you’re asking is generally “what is the minimum number of people required to keep society functioning well”. You kind of define “functioning well” as keeping our industries running as well as progressing, keeping our knowledge preserved, solving major issues like disease/natural disasters, etc. If I bucket each of the groups of people required to tackle these problems into something we call “an industry”, you could naively say it’s a function of “number of critical industries required for society to operate well” (call this NCI for Number of Critical Industries) multiplied by the minimum number of people required to work those industries (call this MRW for minimum required workers) and boom you’re good. The answer is NCI * MRW.

But this doesn’t really work for a number of reasons. Here’s just a few:

• For NCI, you’d need to explicitly define what industries are “critical” and that will vary from person to person. The number will probably shift pretty dramatically over time as the world environment changes or new problems crop up
• The MRW will be different for Critical Industry as every industry should require different amounts of people to work it. This means you should calculate it on an industry by industry basis
• The MRW will decrease over time as new technology and practices give way to automation in each industry. So the MRW on an industry by industry basis will be changing constantly
• The size of required industries will change depending on the total number of people allowed by this society right? So as soon as you decide “ok we’ll need to add another indistry that will require 10000 more people” those new people now need food, shelter, electricity, and transportation which means some of those industries now need to grow. Any change effects every other industry.
• We can never predict what things will cause changes to the NCI. You might consider car manufacturing a critical industry, but one day we may develop teleportation and suddenly that industry will not be needed anymore

There are so many factors here that are just impossible to account for as well as totally subjective. I don’t think people currently can estimate a minimum work force required for one industry (i.e how many teachers do we really need? Doctors? Scientists?) let alone make a good estimate on a societal or global scale.

Honestly whatever question you’re asking seems too abstract/impossible to model to ever really be super helpful.

Given that - idk let’s say 1 billion people