Replaced 12v battery - discovered dangling part and missing duct? (2010 Gen 3)

Hello forum, after considerable reading and preparation (compared to how I normally function), I replaced the 12v battery in my 2010 Prius yesterday and the process was a lot quicker than I expected. After quietly patting myself on the back, I realized perhaps my mechanical skills were not the cause of the quick project, as I considered the following clues:

• A dangling part with one of those plastic connectors that snaps into a hole (pictured below)
• No requirement for a socket extension
• Potential missing ducting (pictured below: the black ducting on the left of the photo above the orange plastic)

I took a few pictures and wondered who had been in my trunk recently. Can you help me (1) identify this dangling part and (2) determine if I am missing other parts? (I expected some ducting connecting to the black plastic vent off the big battery above the orange plastic)

Thanks,
Max

 

Thanks both!