I do NOT want to have to open Chrome browser; I just want to be able to do direct Google search with other tabs still open - like I can do on my windows laptop
Welcome to Android Central! The Google search app doesn't work that way. The way you do it on your Windows laptop is by using a browser, not the Google search app.
You don't. Which is why I just end up disabling the Google app and just search directly on the browser. I just remapped the call search button to immediately open up a browser.