malware

Go step by step and test.

   1. Remove unknown profiles if present.

      System Preferences > Profiles

      Open System Preferences,  select “General and click  the “Profiles” icon ( a checkmark on a gear) .

      When Profiles pane opens, select the unknown profile and click the minus button at the bottom.

      Section: Remove a configuration profile from your Mac

      Profiles: https://support.apple.com/guide/mac-help/configuration-profiles-standardize-settings-mh35561/mac

  2. Remove unknown extensions:  Safari > Preferences > Extensions

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

   3. 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 v4      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.

       Scan for Malware again.

       Additional steps  if necessary.

  4. Reset search engine:    https://support.apple.com/guide/safari/customize-your-search-ibrwe75c2a3c/mac

  5. Reset  Homepage.   https://support.apple.com/guide/safari/set-your-homepage-ibrw1020/mac 

  6. Check proxies. SOCKS?

      System Preferences > Network > Advanced > Proxies

      Deselect   any  proxies if selected.   

   7. Restart your Mac. Relaunch Safari holding the Shift key down. 

It could be a browser extension that is doing this, you may need to see if there are any browser extensions installed, if there are any, you may need to remove them as they could possibly be the source of the problem. Hope this helps.