I found a solution.
“Gutenberg Compatibility Will Only Be Available in ACF Free Version 5.” (see https://www.advancedcustomfields.com/blog/the-state-of-acf-in-a-gutenberg-world/ )
So I upgraded to the early access version of ACF 5 as described here: https://www.advancedcustomfields.com/resources/upgrade-guide-version-5/
After this four simple steps, WYSIWYG fields work as usual in the new Gutenberg editing environment as well.
Another way is to wait for the offical release of ACF 5, which is announced for early September, and activate the Classic Editor plugin and choose under Settings > Writing the Option “Use the Gutenberg editor by default and include optional links back to the Classic editor.” So you are able to edit pages optional with the classic editor till the new version is released.
I choose the upgrade only on my localhost parallel installation (only for testing), not on my live site. On my live site I’ll wait for the offical release of ACF version 5.
Before any upgrade, which could affect the database, I would strongly recommend a database backup.