12/12/2022 (10:08 AM PST): I called AppleCare, and asked for someone in the iOS Department. Unfortunately, the agent's iPhone had an older iOS version, and she told me that Apple does not let employees use their phones for work, so I had her do a screen share with my iPhone. I demonstrated the problem, so she could see that even with the latest iOS update, the Google search window is still disappearing behind the Safari address bar. (Although you CAN now pull it down, tap in it a second time, and start typing, without having it disappear.) I then recited the exact steps to reproduce the bug, which she typed out. She told me that she would send this to her supervisor, who would send it to HIS supervisor, and then his supervisor would send it to the engineers. She also gave me a case number, so if I do not hear back in a reasonable amount of time, I will call Apple back, refer to the case number, and ask to speak to a Senior Advisor, since they are able to contact the engineers directly. I will keep you all updated on this post. Fingers crossed...