In conversation with @William Reynish (billreynish) we found a way to make the Find & Replace a horizontal function, like most modern IDEs, by moving it into the Text Editor footer:
This patch removed the F&S in the sidebar and assigns Ctrl + F to the new operator.
If the toggle operator should be moved into a Pyhon operator, I would need help doing that. I mean in this folder(but currently there is no Text Editor python operator file):
Also I need help to switch it off as default.