You need to configure the Stock Services found at /admin/commerce/config/stock/settings and choose Local Stock for your product variation.
Related topic can be found here.
EDIT: reading your question again and it seems that you added the field to the product itself, instead of adding it to the product variation. Stock field needs to be attached to the ...
As far as I know, there are no supported modules to acheive what you want.
So if you want a sustainable and future proof solution, you should probably code it yourself.
I would go for solution, where I create a custom entity type, Product Validation.
Here are some fields, that I think it should contain:
Product ID (The product it's active on).