How do I log all my browser searches

I'd like to log everything I search for in the browser and the URLs that I click on from the results.l presented to me.

Bonus points if I can save the first page of results I was offered so I can view the options I skipped over.

Does such a browser extension exist? I'm not sure what terms I would use to find such a thing, but it feels like something that someone has probably already done.