Positioning an all purpose ‘smart’ button

I'm building a desktop app which has a kind of smart button. On click, the focus switches into a search bar and a pop up shows up (not a modal box). One may use the search bar to quickly add reminders, empty notes, etc and of course, to search. You get the idea. This is a major feature of the app. And I'm confused about the positioning. My ideas are as follows.

what I did

There is a home screen which you are presented on opening the app. On the homescreen, there is a toolbar, sidebar, main panel, and an area on the right for things like minimal calender, preview of things. On the main panel, there is a searchbar with an icon. Icon is the modifie version of the app logo. This searchbar is the smart button/bar. On click, it shows a pop up which shows the result ofthe search, and more, and has some buttons. The app logo,is on the left of the toolbar,whifh doubles as a dropdown menu for accessing things like open, view, settings etc. If one moves away from the home screen , the smart bar minimizes to the toolbar on the top. Clicking on it brings up the pop up and the minimized smart button expands to the searchbar.

But doing it way totaly confuses the user as there are two similiar looking buttons on the toolbar. Home screen ,moving away from home screen, on clicking the button

alternative

Regardless of the the screen you are looking at, the smart button stays fixed in the toolbar at the center and does the same as the above said minimized smart button. And instead of a fixed logo on the left of the toolbar which doubles an options drop down button, there is just a button for accesing the options. Alternative

First of all, I want to avoid the button on the left of the toolbar if its not a logo or remove any element from there. Thought about putting the options button in the pop up or the sidebar but they are already populated with unavoidable elements.

Any insight on this at all would be greatly helpfull. I have the illustrations but is impossible to upload via the app and the browser keeps crashing as I'm using an old samsung gt s7262 and there is no internet on the pc.