Welcome to the Technical Forum. I tried to find more data on the connectors . I was not able to . There is no pitch or spacing listed.I also do not know what that piece is off of the connector. Here is the link I found:
Though you would need to know the picth . This is measured from the Center of one pin to the center of the next one.
Found on page 24 of the “Installation Guide” for the Bose ESP 880 that they are 3.81mm pitch plugs.
Based on that, here’s a link to the most likely mating plugs.