Some additional info regarding my previous post:
Evernote support sent me a direct link to download the latest version for MacOS:
V. 10.2.4 Build 1949 public
Editor: V 111.0.14414
Service: V 1.21.2
This version works. No loss of all notes once you close and reopen the app. It even can sync with iOS now. To confirm the different behavior, I once again reinstalled the latest MacOS version from the App Store:
V. 10.2.4 Build 458360 public
Editor: V 111.0.14414
Service: V 1.21.2
Complete loss of all notes again. One more time I reinstalled Build 1949 from the support email download link. Everything works. So the App Store version (Build 458360) seems to be broken. Build 1949 is behaving fine so far.