virus?

In addition to removing malware with Malwarebytes, remove any Profile added by the adware.

   1. Remove unknown profiles if present.

      System Preferences > Profiles

      Open System Preferences, 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.

  2. Remove unknown extensions:  Safari > Preferences > Extensions

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

Also check Safari/Preferences/General to see what your Home Page is set to. If Searchpulse, change it.

Safari Homepage setting greyed out 

Download and run Malwarebytes. Malwarebytes was developed by one of our own colleagues here in ASC and is about the most proven anti-malware software for Mac. It’s the only one recommended by Apple tech support folks.