2. Make sure that the text box has a label that says “search” or “filter” and not just a magnifying glass icon. You can only get away with an icon if the GUI toolkit allows you to give it an alt text.
3. Make sure that this label has a hotkey (underlined letter) and that it's properly linked to the textbox so that pressing the hotkey actually focuses it.
4. Make sure that the tree view is next after the textbox in the tab order.
5. Make sure that it's obvious how to cancel a search. You've already assigned Enter to performing the search (as opposed to closing the dialog) which means you can't use Escape because that is already required for closing the dialog. I think one way is to let the user empty the textbox and press Enter to clear the search, but you can also have a separate button as long as it has a hotkey and an alt text if it's just an icon. This kind of button is allowed to sit between the textbox and the tree view in the tab order, but make sure it stays that way and you don't add 10 more buttons there so navigating to the tree view becomes arduous.
I think it's ironic that I can give all of this advice just by being a keyboard user. I'm not visually impaired and I don't use a screen reader.