For the benefit of those of us who are new to Android and unfamiliar with its ways and terms: what do you mean by ‘home screen’?
Do you mean the lock screen that shows when you open the Gemini? (I disabled that, and have largely forgotten what it looks like.)
Or the launcher screen that you get when you tap the circle button on the right-hand side of the screen? (I'm still using the default one, which I believe is referred to as ‘Launcher3’. I've set it up with three screensful of shortcuts to apps, files in Jota+ and AlReader, and Termux scripts. I still think a more powerful App Bar would render the launcher mostly obsolete, though.)
None of the screenshots above look like anything I recognise… What are they showing, what do all the various things do, and how might we set them up if wanted?