Graphics tablet used to work without a third-party driver. How to reenable this?

First, try adding the software you are using with the Tablet to Accessibility. Next, try to determine what is the default driver used by Catalina for your Tablet, and add that too (if possible) to Accessibility.

While this issue is most probably due to architectural changes in Catalina, try disabling "System Integrity Protection" (SIP) and see if it works:

1. Go into Recovery Mode by restarting your computer and holding down the Command+R keys until the Apple logo appears on your screen.
2. Click Utilities -> Terminal.
3. In the Terminal window, type in csrutil disable and press Enter.
4. Restart your Mac.

Be sure to enable it again after you are done testing, following the same steps as above but using the command csrutil enable, once you are done testing.

You can use Activity Monitor to detect if high CPU is happening when you are using the Tablet.

(Otherwise, inform the manufacturer of the tablet that you can't test what they are asking you to do because of macOS Catalina. You shouldn't need to jump through hoops for something they should be doing to ensure the product works as described on macOS, i.e. they should be the one testing the products thoroughly for mac.)