When attempting to start the launcher, it attempts to update, however the update always appears to fail if the runtime location is not ~/Library/Application Support/minecraft/, but is instead formed using a symbolic link to another volume.
It can be manually resolved by moving the required files to the correct location, which I found from this forum post, where they think it is caused by the space in "Application Support".
The nativeUpdaterLog.txt mentioned the error code "Error: Cross-device link" when attempting to move a file from /var/ into the launcher directory. I can't find the full log though, as it was overwritten once I manually moved the required files.
MCL-12204 mentions it fails to run on macOS 10.15, but I'm unsure if this is related, as I had an issue with macOS 10.14. Also MCL-12208 mentions a similar issue. I can't tell if either of them are using symlinks though, if so this may be a duplicate.
It's only on the GM version of Catalina that the error occurred to me (MCL-12204) so I'm not sure if that's really related to Catalina. The runtime is in the correct directory : ~/Library/Application Support/minecraft/ however, my home folder is on an external hard drive.
I have these errors in the logs:
LauncherConfiguration.cpp(213)] Error opening: /Volumes/home/leonov/Library/Application Support/minecraft/launcher/.version, Error message: No such file or directory
PistonUpdate.cpp(403)] Update failed for: launcher.bundle/Contents/Resources/ui.zip, Error: Cross-device link
EDIT:
The .version file is indeed absent. (I know this is an hidden file and I looked for it with the command ls -a in the Terminal).