Just an update for everyone. It turned out the source of the problem was the wp Typography plugin that I had added to the site freshly without noticing the broken sidebar on pages.

https://wordpress.org/support/plugin/wp-typography/

When I disable it, the sidebar displays correctly again. I’m using this plugin on several sites without problems, but with this site it breaks the layout. Tried different settings for the plugin, but couldn’t get it to work.

So I’m simply deleting it and this issue is resolved.