If SciPinion wants to organize the areas of expertise by main and sub-classifications, what schema would you recommend? Is there a standard system SciPinion could adopt?

Journals are subdivided according to key words  so that authors submit the  correct type of articles. I am sure that SciPinion could do the same. There is also a very detailed Library Classification system that is internationally recognized. https://www.librarianshipstudies.com/2015/08/library-classification.html

A combination of keywords and science classifications that web of knowledge uses can be useful

As other commenters have pointed out, there are existing systems to adopt/adapt. Bear in mind that the situation is dynamic, so whichever system you use will require regular (in effect, continuous) updating. If you choose an existing system that is already subject to updates, SciPinion will need to maintain contact and update in response. If you choose a one-and-done system, SciPinion will have to develop its own update program. That could be AI-based or crowdsourced, but will produce results that gradually diverge from any other system's. In any event it will need monitoring. 

I also prefer key words, more flexibility 

Key word is the more easy

I would probably start applying the ERC sectors scheme, with minimal modifications
https://erc.europa.eu/sites/default/files/2023-03/ERC_panel_structure_2024_calls.pdf

For me, it would make sense to use Fields of Research and Development (FORD) as main and either expertise or keywords as sub-classification.
As a multidisciplinary researcher, even though I am a specialist in scientific image analysis, I could fit in many FORDs - but only in a few keywords.

Classification should ideally be done using generic keywords (umbrella terms for specific fields) and sub-terms for subdivisions. For instance, you could classify expertise as cancer/oncology for any mild, malignant, or metastatic tumours, then you could divide by tissue type, which is the predominant approach used for specialist and expertise training, (e.g., lung, breast, colorectal, etc.). 

Key words is the more easy