Animation would still play in the viewport.
There are two ways to unlink an action from the Outliner:
[1] `Unlink Action` on the Animation Data context menu.
This does `outliner_do_data_operation` / `unlinkact_animdata_fn` and has
the correct DEG update.
[2] `Unlink` on the Action context menu
This does `outliner_do_libdata_operation` / `unlink_action_fn` and was
missing the DEG update.
Now add the missing DEG update to the second case.
Maniphest Tasks: T95679
Differential Revision: https://developer.blender.org/D14089
b4a2096415