Safari works for a short time and then stops opening new sites. Any ideas

1 Startup in Safe Mode and test Safari.

Restart normally by clicking the "Restart" button at the bottom of the screen.

Test Safari.

Use safe mode to isolate issues with your Mac - Apple Support 2.

2. https://support.apple.com/guide/safari/if-you-cant-open-a-website-ibrw.1071/mac

3. Remove unknown extensions:  Safari > Preferences > Extensions

      https://support.apple.com/guide/safari/use-safari-extensions-sfri32508/mac

4. Check for adware.

       Run the latest release of Malwarebytes for Mac to remove malware/adware, if installed on your Mac.

       For instructions:  Install Malwarebytes for Mac          Uninstall Malwarebytes for Mac

       Click the “Scan Now” button. Once done, quit Malwarebytes for Mac.

       Restart the computer and relaunch Safari holding the shift key down.

Also try another admin user account.

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