Resolved? Yes and no.
Yes: I used the code in your reply
https://generatepress.com/forums/topic/read-more-label-in-search-result-page/#post-211142
which solved my excerpt and read -more- problem.
Thank you very much for this!
No: I try again to explain.
My objective is to have almost similiar result pages for:
Searches, e.g. https://insoguide.de?s=insolvenzverschleppung
Blog page: https://insoguide.de/news
and Tag page: https://insoguide.de/thema/insolvenzeroeffnungsgrund
As you see, only the tag page looks different – it would be nice if the posts and pages would be presented in a masory style.