Is it possible to have global search on New Experience in Document Library

[SharePointPro]

With the new experience for a document library, we have a search box  that searches the document library.

Is it possible to put a search box in the header for global search?

Similar to to classic pages

[#2]

If you are in the document library, the search box searches in the document library...but you also have a search box in the home page of the site that searches in all the site...by the way, coming back to your question the only way I can think you could achieve this is by means of a SPFx Extension. As you know, SPFx extensions provide the only way to customize modern SPO pages

[#3]

The client doesnt want to click "BACK" or "HOME" they want to be able to search directly from the document library page..

I'm not able to put a SPFx extension into a Document Library page am I? Only onto a normal page?