UI - Fix Task Instance note refresh when clearing a TI with a note

[pierrejeambrun]

Body

Video example here: #53069 (comment)

Currently when we clear a TI and add the node, we invalidate the query cache correctly.

On the other hand in the TaskInstance/Header.tsx component we use a note state to handle the input.

This state is not refreshed when the TI is refreshed from new cache value and keeps reference to the old value.

Expected behavior:
We should still be able to edit the node with the EditableMarkdownArea, but if the input is not dirty (no typing made) then if the TI change it should be reflected in the displayed value.

Committer

• I acknowledge that I am a maintainer/committer of the Apache Airflow project.

[Jasperora]

Hi, I would like to help this issue. Could you assign it to me?

[pierrejeambrun]

Of course, thanks @Jasperora you're assigned.