Fully display Search panel including the Find Button

Jon's layout suggestion (reply above mine) is the simplest way, but if you find that changes more things than you want it to, you could instead replace the Tools > Find Files menu item with this:

(It doesn't have a hotkey defined, so if you do replace the old menu item, give the replacement the Ctrl+F hotkey by editing the menu item after adding it.)

For reference, it runs this script, and you can edit the 3rd line to change the minimum width:

function OnClick(clickData)
{
	var minWidth = DOpus.DPI.Scale(800);

	var cmd = clickData.func.command;
	var lister = cmd.sourcetab.lister;
	var width = lister.right - lister.left;
	
	if (width < minWidth && !cmd.IsSet("UTILITY=Find,Toggle"))
	{
		cmd.RunCommand("Set LISTERSIZE=" + minWidth + ",+0");
	}

	cmd.RunCommand("Set UTILITY=Find,Toggle");
}