Been a problem for me for a long time- not sure if it’s a known issue or something I don’t know about but very frustrating.
The “search” field in the window tool bar doesn’t allow scrolling when the text is longer than the window; so I can’t see the full search string or get to the end to add to it.
I agree the Full Search window is better and that’s what I’ve reverted to (much larger search field.
But be aware, the right arrow to move beyond the end of a full search field doesn’t work (using Safari-Version 8.0.4 (10600.4.10.7)- for either a Search window or a regular document window
I’ll turn it in again as a bug- but this has been around a long time.