although I don't really know how "knowing which addresses belong to the same wallet" would be harmful or not
My usual anser is: "it depends". If you want to be absolutely sure no chain analysis company can access this data, you shouldn't use a public Electrum server. But considering Electrum's popularity, I don't think that's a concern to most people.
When you use Bitcoin Core, you can also reduce your privacy by linking different addresses together on-chain.
on the fly space is 12 GB but data download has to be 720 Go anyway, isn't it ?
Correct.
And how much Go is the blockchain update by month, once first pruned is ok, is it ike 10 Go new data download ?
I think it's about 1-2 GB download per week. But if you allow incoming connections so your node is also uploading, you can transfer much more data.
"Bitcoin Core is indeed more private, especially if you run it over VPN/Tor."
--> will try my best to go for it
As always, privacy comes at a cost. I wouldn't do it with less than 16 GB RAM, and memory consumption only gets worse in the future.
Have you heard about AirGap ?
A quick search shows it's "an offline phone". I wouldn't risk my money on that.