I just accidentally found a way to remove the Google Search bar while using Quickstep and Google active:
I associated the search bar with Startpage to be my default search engine when configuring the phone for first use.
Later I got tired of Startpage looking like a full blown browser and not only a search engine and I uninstalled it. Now I have “Samstag, Okt.25” instead of the search bar in big letters at the top. Which is good as I can read it without glasses This remains after reboot and I am quite happy with this.
I did also add the Google search widget elsewhere, without interfering with the day & date display.
(I found some some similar threads, but all closed, so I started anew.)
Thats why I dont use the setting, as I like the date there and have the Google App disabled from the beginning. However many people didnt want the date.