CTRL+F brings up the Find popup with the focus on the Find: field.
However, if I edit a bit in the document, then hit CTRL+F again, it shifts the focus to the already-open Find popup, but not the to the Find field. Any typing is lost. Irritating!
Focus returns to the open dialog wherever you left it. If you type in the Find field and use Enter to search for the word rather than clicking the “Next” button, after typing in the editor, Ctrl+F should return you to the Find dialog with the insertion point blinking in the Find dialog at the end of the text already there. You can also use Tab or Shift-Tab to move focus in the dialog, so e.g. if you do return with focus on the Next button, Shift-Tab twice will return to the Find field, with the current search term highlighted.