I installed WPML version 4.4.5 and Site Kit continues to have the problem of disconnecting credentials!
In my opinion it does not depend on WPML, but on the fact that Site Kit does not record all the variables concerning the connection with the Google account (example: https://www.example.com/en/ + https://www.example.com/de/ + https://www.example.com/fr/ + etc.). Whenever the language is changed, the connection must be restored as Site Kit no longer recognizes the authorization given by the Google account. In practice, the problem arises from the fact that the connection registers the URL to which authorization is given including the linguistic extension (…/en/, …/de/, …/fr/, etc.). From here, after changing the language, the URL changes and Site Kit no longer recognizes the credentials for the connection. This forces the user to have to log back in every time he wants to analyze the data. To make Site Kit work on a site with WPML it is therefore necessary to modify the way to authorize the URL, making sure that this is provided only on the domain (www.example.com), without linguistic extension. In this way, whatever linguistic extension you want to use, Site Kit will always and only recognize the domain and can therefore work in any case.
I hope these guidelines will help insiders get the Site Kit plugin to work properly with any language.
We are all looking forward to a solution.