Last week we updated the look of Search on desktop to mirror what's been on mobile for months. We've heard your feedback about the update. We always want to make Search better, so we're going to experiment with new placements for favicons.... — Google SearchLiaison (@searchliaison) January 24, 2020

Over the coming weeks, Google says, it will continue to test changes. Desktop users will see a variety of favicon placements. It's hard to say at this point what that will look like. It's also unclear how Google will differentiate ads.

Last year, Google brought the favicons to mobile Search. The goal was to make it more evident where info is coming from. According to the company, the changes have been well received on mobile. Google says early tests for desktop were positive, too, but that the company is "always incorporating feedback from our users." In other words, Google seems to have heard your complaints, and it's working to figure out the best way to redesign its desktop Search.