This is normal. Deleting an object from the scene doesn't immediately remove it from Blender.

However, objects without users are not saved to the .blend file. You should find that the armature is gone after you reopen the file.

If this is not the case, then it still has a user, or has a fake user.

Define "normal", was it a bug before? As said 3.1 did behave differently under the same conditions. The condition is deleting it from the viewport.
The 3.2 version only deletes it of the project if it's been selected in the Scene Collection instead of viewport.

Normal means that it's intended behaviour in the core Blender application. This has nothing to do with the Blender Source Tools, which doesn't handle deletion of objects or set fake users (except on import, for Actions).

That’s weird, cause there defo is a different in behavior in the different BST versions. I went through a few commints, but couldn’t anything that would have caused it, but something defo changed it.

Are you using two different versions of Blender?

I'm not. I just tried every commit and the behavior changed on Mar 20, 2022 in this commit: https://github.com/Artfunkel/BlenderSourceTools/commit/b1c6144e4a621d2975ebec2f91acc78bd97ec187

It's the new PointerProperty which changes behaviour. It adds a user to each object in the scene export list and thus causes Blender to not delete them from the Blend file when they are removed from the scene/view layer. (I was evidently wrong when I said that deleted objects remain in the Blend file until it is closed.)

Immediately after the object is removed the scene's export list is updated, the PointerProperty is removed, and the user count is decremented. But by this point Blender has already decided not to delete the object fully.

The extra user is annoying, but I'm not in a rush to change this. Even if I did change it, you still cannot assume that deleting an object from the scene will remove it from the Blend file: the object could have additional users for many reasons, e.g. from modifiers, other scenes, or a fake user. You should keep the changes you made to your script.

I'm glad to know now why this is happening. I will defo keep the changes to the script, even if you would change it. This showed that many people don't tend to update their addons, so I can imagine that many would also stay on BST 3.2.2 even after an update.
Thanks for your time!