I've figured this out! I understand this thread is kinda old, but I'm leaving this here for those who don't exactly wanna see their History and Bookmarks pop up in their searchbar; this works for both normal Opera and Opera GX, assuming you're opted into Beta features
Type in "opera://flags" and switch that "nice, neat, and very nifty" (sarcasm implied) feature "Address bar dropdown categories" from Default to Disabled.
Nice, quick, and unbelievably and annoyingly hard to find if it wasn't for the fact I stumbled on a normal Opera thread on a whole different site and found my solution there. I even went through the effort of creating an account here to put this here so others who don't really like seeing their bookmarks and history be displayed for the world to see (assuming you're streaming your desktop) could disable it. Glhf with never seeing "Bookmarks, History, Opera" in your searchbar again and only your searches!