safari doesn't work with Catalina.. how do you fix it?

What isn't working properly? More information would help.

Are you running any anti - virus programs? Using a VPN?

Try setting up another admin user account in System Preferences/Users & Groups to see if the same problem continues.

Isolating an issue by using another user account 

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin

Etrecheck – System Information

Web site version if required.  https://etrecheck.com

Startup in Safe Mode   https://support.apple.com/lv-lv/HT201262

To exit Safe Mode, click the Restart button at the bottom of the screen.

Launch Safari holding the Shift key down. 

Test.