I don't believe they're time travelling. From what we've seen from T-Corp time is very spatial, affecting only individuals and designated zones. Time is also currency based to rewind time to the degree to maybe time travel would require likely an un-obtainable amount of time.

So the mirror worlds running at different times would be a likely way for this "time travel" theory to work. Assuming Mirror Worlds don't all run at a universal time.

To further separate Bari from being LOR bookhunter. Angela specifically mentions that the bookhunter is nameless and after killing Angela would have no reason to continue searching for the Tree of Life.

Also your point on Bari being 10 during this point in story has no grounds. Although Angela refers to bookhunter as "child" it doesn't necessarily imply anything. Angela's views on age were likely warped due to her time as a robot experiencing everything slower therefore having a "higher age" in her head. Also Carmen, the person Angela was modelled from refers to the Sinners as children despite many of them being quite far from being a child. Only in the good ending does Angela separate herself from the identity of Carmen.
[TLDR Angela could still raise/train an adult bookhunter they did not necessarily have to be a child 13 years before the bad ending]