I found the culprit: the AsyncJavascript plugin. If I set it from Async to Defer, I can use the Customize layout again.
However, this dramatically impacts the server response time. I am consequently wondering if I will not set the plugin to Defer only when I have to modify the website’s layout. What do you think?
As long as I know how to activate the website layout in Customize, I am fine.
One other probable cause for the increase in server response time once I had set AsyncJavascript plugin to Defer is that I had no Page Rule in Cloudflare to “cache everything.”