Theoretically, and I have not tried it myself, you can get the current node using an AnimationNodeStateMachinePlayback resource and use the get_current_node
function, at least based on the documentation. This will return a string with the current animation node, which I would assume, though I am not sure how, you could use to get the animation directly, and then from there you could figure out how far the animation has played. Looking at the documentation though, I see how you can get the current animation as a string, but not the position of the currently playing animation (or even the animation itself).
It might be worth posting this on the other Godot communities, like Reddit, Facebook, Discord, etc and see if the developers there know. I haven't poked around with the AnimationTree or the source code enough to know how to figure out a solution to this issue, but Godot developers more familiar with the node and/or source code may be able to shed light on the issue.
If no one knows or you do not get any answers, even on other Godot communities, I would suggest opening a proposal to add a way to get this information from an AnimationTree node to the Godot proposals repository.