While you can keep going with fewer, the diversity of your economy would be lower and your progress slower.

For example I suspect you would have a lot fewer exotic fruit in your diet with 2 billion people. In the same way you will have fewer people researching the various types of batteries, and slower improvement over time.

The service economy is the part of the economy which is all about people helping each other, so with fewer people would mean fewer needed but again expect less diversity in the services that are available to you.

Same with manufacturing - a smaller population would have a less diverse range of products.

Some projects which are affordable in a large economy would not be affordable in a small economy, for example a space elevator which costs 5% of the world economy may be affordable, but one which was 30% would not be.

So for this question:

> what's the minimum population required for preserving all our knowledge, technology, and even progressing further, doing research and implementing results.

Probably not that many, but don't expect life to be the same qualitatively, and don't expect research to progress half as fast.