Add a ▶ button next to the text area for mouse-based submission.
Extract shared doSubmit() on the input RowLayout. Button uses
focusPolicy: Qt.NoFocus so it doesn't steal focus from the TextArea.
Replace MouseArea overlay with TapHandler inside TextArea.
The MouseArea sat on top and intercepted left-button press events,
blocking click-and-drag text selection. TapHandler cooperates with
the TextArea's built-in selection handling.