It seems to be the keychain.
What Apple asked me to do was to remove my Apple ID from a device and test another Apple ID.
Then it was working (access to the app without the search).
What is great after, was to recover my iPad. The iCloud Photos wanted me to pay the superior tier of storage because it says 20GB of pictures was on the iPad. But it was the iCloud Photos pictures.
Apple is stealing people with this. With 2 to 7$ more, even for a month, with millions of customers, this means a lot of money!
And still, they don't know how to reset a keychain !
And anyway, I don't want to loose all my datas : sorry guys but the problem is with this stupid HOME app, no link with my IMAP, POP, SMTP and WIFi passwords!
They should just fix this.