Hi Liz and thanks for the great pictures of your sap-leaking Monkey Puzzle tree. I just planted one myself, so I was really curious to see the answer to your question. And... I can't really find a good one! Some sites say it is a normal part of the tree, cut off the brown branch and wait for the next season. Some sites say look for holes or injury under the sap to see if there are insects at work or someone has damaged the trunk. Other sites say there are no borers that would make this much of a hole for this tree.

The most recent post from another expert says basically to wait it out and see what happens. This expert thinks the tree was stressed and this is the reaction. Your tree may not have gotten enough water this summer with that burlap still in place which would definitely stress it. I would remove as much of the burlap as you can by carefully digging around the roots and then wait and see what spring brings. If you want to pull off the sap and look for holes or damage, that would be OK. You could also call around to see if there is an arborist anywhere who knows about Araucaria araucana trees. Here is the question and answer from last year:
https://ask2.extension.org/kb/faq.php?id=765945

And for fun and laughs, here is an exchange from someone who wanted to collect the sap and all the answers he got from around the world trying to identify the tree, figure out how to use the sap and even trying to get the correct terminology for it! Enjoy:
https://bushcraftusa.com/forum/threads/tree-sap.175349/