MacBook Pro keeps shutting down

See if your laptop qualifies for any of the free Apple repair programs listed here (especially the SSD & battery programs):

https://support.apple.com/exchange_repair

Run the Apple Diagnostics.

You can always check the condition of the battery by Option clicking the battery icon on the menubar. Any condition other than "Normal" or "Good" means the battery should be replaced.

Run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper.

While the Apple Diagnostic assessment of your battery sounds like an ordinary loss of capacity, it is a bit odd that the Battery condition within macOS doesn't reflect it. I've found the macOS Battery condition typically matches what the Apple diagnostic reports except when the battery may have an internal fault. Maybe Catalina changes this behavior. The diagnostic information regarding the battery doesn't sound like you would have any sudden shutdowns, but it cannot be completely ruled out.

If you have any external devices connected to the laptop, then disconnect them to see if you still have the problem.

Have you run Disk Utility First Aid on your drive?

You may want to make sure you have good verified working backups, then perform a clean install of macOS to test whether the issue still exists without any third party apps or customized settings. Do not migrate anything or restore from a backup until you have confirmed whether the clean install fixes the problem. If a clean install fixes the problem, then most likely you are dealing with a software, settings, or corrupt preference file issue. Use these instructions as a guide to perform a clean reinstall of macOS.

https://support.apple.com/kb/HT208496

I would suggest erasing the physical drive instead of the volume as indicated so a whole new partition table is created/refreshed. To see the physical drive in Disk Utility you may need to click on "View" and select "Show all devices" before the physical drive will appear in the left pane of Disk Utility.

Since you did not include the complete EtreCheck report, I would suggest you take the laptop to an Apple Store or an Apple Authorized Service Provider to be examined. Many times knowledgeable contributors will see things in the report which can cause problems even if the report doesn't specifically call them out as harmful.

I've seen this as well on several different laptops in our organization. The best you can do is report the issue to Apple or if you have tried everything I mentioned previously and are still having problems, then take the laptop to an Apple Store or an AASP to be examined.