Using 'Clean My Mac' and got this in the system log

Uninstall CleanMyMac from your Mac. It only causes more harm than good and you may end up removing things that shouldn't be removed. Safaridavclient is a system launch agent for Safari, and you do not have write permissions. I would remove the app by following these directions: https://cleanmymac.com/how-to-uninstall-cleanmymac-3

The only scanning tool that you might consider is Malwarebytes, but macOS has its own security and does not require third party cleaning tools or virus scanners.

Some of the most common sources of the software-related problems arising for macOS folks and that get posted around the forums are caused by add-on anti-virus apps, add-on anti-malware apps, add-on cleaners, add-on firewalls, and add-on VPN clients.

You also seem intend on clobbering a part of macOS that macOS itself is clearly trying to protect.

Ponder where this delete-first-ask-questions-later approach might end.

I too would remove this cleaning app.

Oh, and that SafariDAVClient file is a hunk of Safari. Likely a preferences file related to that hunk, based on the name.

Uninstall CleanMyMac. It is not needed.

You can check to see if you've removed all of the files by downloading and running Find Any File to search for any files with the application's name  and the developer's name in the file name.  For example for CleanMyMac software you'd do the following search: 

1 - Name contains cleanmymac

Any files that are found can be dragged from the search results window to the Desktop or Trash bin in the Dock for deletion.

FAF can search areas that Spotlight can't like invisible folders, system folders and packages.

In the future don't ever run any "cleaning", "optimizing", "speed-up" or anti-virus apps. They are totally unnecessary. Read this user tip for what you should do: Effective defenses against malware and other threats - Apple Community.

Easier to shut off the Catalina update notifications, if that was bothering.

And a backup and re-install is locally preferable to the add-on cleaners. The Migration Assistant data migrations work quite well, and are something Apple directly supports as that’s (also) how you migrate to a new Mac. Good way to clean up the old stuff, too.

To rebuild the boot and performance caches and such, boot into Safe Mode. Then reboot normally. Some add-on app rebuilding the macOS caches only means the caches get rebuilt. Or the Mac will be running more slowly, because those caches are performance optimizations intended to cache frequently accessed data.

Who suggested to do the CleanMyMac thing, how credible were they.

And, oh dear you paid for it....

The system volume is mounted Read Only on Catalina. It doesn't matter what junkware you use to try to remove it.