Select all your photos. Right Click (or control Click) and select "Play Slideshow". It will force to download. Solved.
Thank you bertan for the hint, selecting all (85'000) photos and starting a slideshow showed a lot of errors in the log console. Especially the raw photos from my Nikon Coolpix 5400 seem to be no longer supported in Catalina and prevent Photo to complete it's downloads. I'm now converting those unsupported NEFs to fine working DNGs and see if that helps. Probably I have to fix other photos that show errors in the log.
PS: Finding the affected photos in the Photos app is since macOS Catalina a bit demanding. In the log console and the library all assets (like photos, videos, etc.) are referenced with a UUIDs (e.g. A92A8F30-CA44-42CE-8F00-D5CFA4232768). Their corresponding filenames (e.g. DSCN2268.NEF) are "hidden" in Photos database (˜/Pictures/Fotos-Mediathek.photoslibrary/database/photos.db). But only this filename is searchable in the Photos app. So to lookup the corresponding filename I opened the photos.db with SQLiteStudio (and closed the Photos app before to avoid conflicts). The UUID seems to be stored in table ZGENERICASSET column ZUUID where column ZADDITIONALATTRIBUTES points to the primary key Z_PK in table ZADDITIONALASSETATTRIBUTES where column ZORIGINALFILENAME shows the original filename. Just to let you all know how to find assets in error that can prevent Photos from running normal...
PS2: Be aware that when reimporting those NEFs as DNGs all GPS metadata is lost (at least in my workflow). I had to embed those GPS tags with exiftool into the DNGs from their XMP sidecar files... (e.g. exiftool -fixBase -m -tagsfromfile %d/%f.xmp ./*.dng -o output/)
This update to Catalina is keeping me quite busy...