I checked again more in depth now. Of course disabled all plugins and used WP default theme again.
The cause of the empty select labels is actually not the plugin “Preferred Languages” but solely selecting “de_DE_formal” as the main site language. Switching it to “de_DE” will show the labels again. Please make sure to enable “Deutsch (Sie)” as the main site language not “Deutsch” as shown in your screenshot to replicate the issue.
We use “Preferred Languages” to provide a fallback in case plugins don’t support the formal language code btw. This works most of the times.
However, I dunno if this is the right approach in order to correctly process and translate content written in formal language with Deepl. Maybe this is not even relevant for the API-calls.
After this fix, I was finally able to translate some content. Yaih!