This is next level weird.
I found this How to configure connected mode in VSCode - #7 by locdangle2552 - which totally breaks the setup
It truly seems we can NOT have open several folders (each folder a project in an org) at the same time in VSCode without actually breaking the SonarCloud integration, unless we bind ALL those folders to the same project, which is totally undesirable
This means, we have to open each folder (which corresponds to a project in Sonarcloud) on its own.
how cumbersome.