The TextArea does consume the Tab key and adds a tab to the text, however it does not consume the Shift+Tab combination, which is in my opinion slightly confusing.

Especially if the TextArea is set to not being editable (setEditable(false)), the focus can travel via the keyboard into the TextArea, but can only leave it again with Shift+Tab, because Tab is consumed but because the TextArea is not editable, nothing happens.

Ideally the TextArea should have an option if the tab is used for inputting text or as focus traversal mechanism, but it would already be enough if the behavior for Tab and Shift+Tab is "synchronized" (meaning either both work, or none).