How to solve Search marquis bug from browsers ?

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 the Mac. Relaunch Safari holding the Shift key down. 

If Safari's home page is stuck

In some cases, after being changed by adware or malware, Safari's home page can become stuck. You will be able to edit the Homepage field in Safari's preferences, but the change will not stick. This appears to be a bug, and there is an odd workaround. Try this:

1. In Safari, choose Preferences from the Safari menu.

2. In the window that opens, click the General icon (if necessary)

3. Enter your desired home page in the "Homepage" field, but DO NOT press return!

4. At the top of the window, click any of the other icons (eg, Tabs, AutoFill, etc).

5. You may see a prompt asking for confirmation for changing the home page. If so, confirm.

6. Switch back to the General page and check to make sure the home page has been changed.

Credit: thomas_r

https://forums.malwarebytes.com/topic/236261-how-to-remove-weknow-malware-and-others/