I had the same issue and find a solution to it. I'm not sure if this solution will always work but for now it's fine:
I discovered that after setting the focus via code when I press the Tab Key the focus will be in the textbox. Maybe the Fluent Textbox consists of the icon in front of it an the textbox itself. Setting the focus brings the focus only to some invisible control
and sending a TAB brings it to the textbox.
In my code I use the following snippet:
TraversalRequest request = new TraversalRequest(FocusNavigationDirection.Next);
Where _SearchText is a Fluent TextBox