Mac OS Catalina upgrade / install issues

Based on the screenshots, it appears Flash Player isn't completley uninstalled and there's some Flash Player artifacts left on the system, or possibly still in Safari memory.  If Flash Player is completely uninstalled, the version check chiclet would not return a version:

Please try the following:

1. Download the uninstaller: uninstall_flash_player_osx.dmg
2. Download the installer: Flash Player for Safari and Firefox - NPAPI
3. Print or save as PDF the FAQ Where do I find the Flash Player installation log on the Macintosh? section for obtaining the install.log and FlashPlayerInstallManager.log files (ignore the other 2 files listed in the FAQ)
4. Exit out of all applications that may use Flash Player (restarting the system and deselecting 'reopen windows when logging back in' is the best way to ensure applications that may use Flash Player are not running)
5. Ensure applications that may use Flash Player are completely exited out of and run the uninstaller downloaded in step 1
6. After the uninstaller completes, check the /Library/Internet Plug-ins directory for Flash Player.plugin and flashplayer.xpt files.  If either of these are present, delete them and empty the trash folder
7. Restart the machine, ensuring to deselect 'reopen windows when logging back in'
8. Configure your sytem to obtain the logs written to install.log and FlashPlayerInstallManager.log files as noted in the FAQ in step 3.
   1. This is in case there is an error when you run the installer in the next step.
9. Run the installer downloaded in step 2
10. If installation fails, gather the files from step 8 and upload them to Cloud Documents (see How to share a document), or some other file sharing service of your choice that doesn't require account log in, and post the link to the uploaded files in your reply.

What browser (including version) are you using?

If you go to System Preferences, is there a Flash Player item listed?  If so, click on it to launch the Flash Player Settings Manager and then navigate to the Updates tab.  What is the NPAPI and/or PPAPI version listed, if any?

Example: