In the latest versions of BST you can no longer export animations from a linked rig with Library Overrides.
To recreate this issue:

1. Create a blend file and create a collection in the scene root.
   
2. Create the simplest model possible (2 monkeys, cubes, whatever) and rig it in the simplest way possible (1 root bone and 2 bones for objects).
   
3. Save the file.
   
4. Create another blend file and LINK the collection from the previous file, containing the rig (File -> Link)
   
5. Select the linked collection and do Object -> Library Override -> Make.
   
6. Create an action for the now pose-able armature and a simple animation.
   
7. Try exporting the said animation. It will simply not show up in the list and Scene Export will throw

The "Source Engine Exportables" list does show the required Actions, but even if I select it - the "Export" button doesn't show it in its menu and I cannot uncheck checkboxes to exclude other linked stuff (because the checkboxes are grayed out) I do not want to export and which are actually causing the export error (linked meshes and so on).
It seems like purely a selection issue, because if I uncheck all the checkboxes with python and then check the action I want to export and click "Export Scene" - everything works fine.
This did work in BST 3.1.1 - 3.2

I BEG OF YOU, please explain what's going on or fix it, because this is the only sane way to properly animate complex rigs or any rigs in general.
I can't use older BST versions, because they no longer work with the new Blender and I can't roll back to older Blender version for various reasons.
(FYI appending the armature regardless of its complexity 5 quadrillion times to 7 quintillion different blender files is an absolute brain ret@rdation).
The proper way of animating in Blender and any other software ever since Softimage XSI came out is creating a rig in a clean file and then linking it to other files where you create various animations.
Thank you in advance, feel free to contact me at any time.