For anyone interested in doing this, just a small but very important PSA:
Do NOT EVER move the installation of MSFS through Steam BEFORE changing the name of the “Official” folder or the folder’s name where all the packages are.
I am just in a totally stupid situation (Steam’s fault I would say) that I have to re-download everything again.
I think it’s the same issue as people reported THREE YEARS BACK that happens if you VERIFY the MSFS installation through Steam. At least I’m glad that I learned about this, so I’ll avoid it in the future.
TL;DR:
If you want to move your base installation using the Steam interface, FIRST go to your Packages or “Official” folder and change its name. Just call it whatever you want, so Steam won’t be able to find it and simply delete it. After that, when launching MSFS it should ask as usual where the folder is and you’ll can rename it and locate it. Will save you HOURS of trouble.