Unable to open files locally for M365 / SharePoint

I have a problem with opening documents from SharePoint with the function "Open in App". I can see the documents (Word files) and I can also see the option "Open in App" in SharePoint Online - but once I open it using "Open in app" then the local word installation starts (and shows the word splash logo screen) but then the document is not opened. Can anyone help me out with this problem?